x4y – 8xy + 3xy2 = 9 Find dy/dx by implicit differentiation.
> Show that the normal line at any point on the circle x2 + y2 = r2 passes through the origin.
> Find equations for the tangent line and normal line to the circle at each given point. (The normal line at a point is perpendicular to the tangent line at the point.) Use a graphing utility to graph the circle, the tangent lines, and the normal lines. x2
> x2 + y2 = 25 (4, 3), (-3, 4) Find equations for the tangent line and normal line to the circle at each given point. (The normal line at a point is perpendicular to the tangent line at the point.) Use a graphing utility to graph the circle, the tangent l
> Use a graphing utility to graph the equation. Find an equation of the tangent line to the graph at the given point and graph the tangent line in the same viewing window.
> Use a graphing utility to graph the equation. Find an equation of the tangent line to the graph at the given point and graph the tangent line in the same viewing window.
> 3xy − 4 cos x = −6 Find d2y/dx2 implicitly in terms of x and y.
> Find the derivative of the function.
> 7xy + sin x - 2 Find d2y/dx2 implicitly in terms of x and y.
> xy – 1 = 2x + y2 Find d2y/dx2 implicitly in terms of x and y.
> x2y – 2 = 5x + y Find d2y/dx2 implicitly in terms of x and y.
> x2y – 4x = 5 Find d2y/dx2 implicitly in terms of x and y.
> x2 + y2 = 4 Find d2y/dx2 implicitly in terms of x and y.
> Find dy/dx implicitly and find the largest interval of the form –a < y < a or 0 < y < a such that y is a differentiable function of x. Write dy/dx as a function of x. cos y = x
> Find dy/dx implicitly and find the largest interval of the form –a < y < a or 0 < y < a such that y is a differentiable function of x. Write dy/dx as a function of x. tan y = x
> Use implicit differentiation to find an equation of the Show that the equation of the tangent line to the ellipse
> Use implicit differentiation to find an equation of the Show that the equation of the tangent line to the ellipse
> Explain why the derivative of x2 + y2 + 2 = 1 does not mean anything.
> Find the derivative of the function.
> Write two different equations in implicit form that you can write in explicit form. Then write two different equations in implicit form that you cannot write in explicit form.
> Find an equation of the tangent line to the graph at the given point. Kappa curve
> Find an equation of the tangent line to the graph at the given point. Lemniscate
> Find an equation of the tangent line to the graph at the given point. Astroid
> Find an equation of the tangent line to the graph at the given point. Cruciform
> Find an equation of the tangent line to the graph at the given point. Circle
> Find an equation of the tangent line to the graph at the given point. Parabola
> Folium of Descartes: x3 + y3 - 6xy = 0 Find the slope of the tangent line to the graph at the given point.
> Find the slope of the tangent line to the graph at the given point. Bifolium: (x2 + y2)2 = 4x2y
> Find the slope of the tangent line to the graph at the given point. Cissoid: (4 - x)y2 = x3
> Find the derivative of the function.
> Find the slope of the tangent line to the graph at the given point. Witch of Agnesi: (x2 + 4)y = 8
> x cos y = 1, (2, π/3) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> tan(x + y) = x, (0, 0) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> x3 + y3 – 6xy – 1, (2, 3) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> (x + y)3 = x3 + y3, (-1, 1) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> 3x3y = 6, (1, 2) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> xy = 6, (-6, -1) Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.
> (a) find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> Find the derivative of the function.
> (a) find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> (a) find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> (a)find two explicit functions by solving the equation for y in terms of x, (b) sketch the graph of the equation and label the parts given by the corresponding explicit functions, (c) differentiate the explicit functions, and (d) find dy/dx implicitly
> Find dy/dx by implicit differentiation.
> y = sin xy Find dy/dx by implicit differentiation.
> cot y = x - y Find dy/dx by implicit differentiation.
> csc x = x(1 + tan y) Find dy/dx by implicit differentiation.
> (sin πx + cos πy)2 = 2 Find dy/dx by implicit differentiation.
> sin x + 2 cos 2y = 1 Find dy/dx by implicit differentiation.
> Find the derivative of the function.
> x3 – 3x2y + 2xy2 = 12 Find dy/dx by implicit differentiation.
> Find dy/dx by implicit differentiation.
> x3y3 – y - x = 0 Find dy/dx by implicit differentiation.
> x2y + y2x = -2 Find dy/dx by implicit differentiation.
> x3 – xy + y2 = 7 Find dy/dx by implicit differentiation.
> 2x2 + 3y3 = 64 Find dy/dx by implicit differentiation.
> x5 + y5 = 16 Find dy/dx by implicit differentiation.
> x2 - y2 = 25 Find dy/dx by implicit differentiation.
> x2 + y2 = 9 Find dy/dx by implicit differentiation.
> How is the Chain Rule applied when finding dy/dx implicitly?
> Find the derivative of the function.
> Explain when you have to use implicit differentiation to find a derivative.
> In your own words, state the guidelines for implicit differentiation.
> Describe the difference between the explicit form of a function and an implicit equation. Give an example of each.
> Let k be a fixed positive integer. The nth derivative polynomial. Find Pn (1)
> Let f(x) = q1 sin x + a2 sin 2x + ∙ ∙ ∙ + an sin nx, where a1, a2, . . ., an are real numbers and where n is a positive integer.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If y is a differentiable function of u, u is a differentiable function of v, and v is a differentiable function of x, then.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If y is a differentiable function of u, and u is a differentiable function of x, then y is a differentiable function of x..
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
> The linear and quadratic approximations of a function f at x = a are P1 (x) = f’(a)(x - a) + f(a) and P2 (x) = ½ f’’(a)(x - a)2 + f’(a)(x - a) + f(a). (a)Find the spec
> f(t) = (9t + 2)2/3 Find the derivative of the function.
> The linear and quadratic approximations of a function f at x = a are P1 (x) = f’(a)(x - a) + f(a) and P2 (x) = ½ f’’(a)(x - a)2 + f’(a)(x - a) + f(a). (a)Find the spec
> f(x) = |sin x| Use the result of Exercise 114 to find the derivative of the function. Answer: f(x) = |sin x|
> h(x) = |x| cos x Use the result of Exercise 114 to find the derivative of the function. Answer: h(x) = |x| cos x
> f(x) = |x2 - 9| Use the result of Exercise 114 to find the derivative of the function.
> g(x) = |3x - 5| Use the result of Exercise 114 to find the derivative of the function.
> Let u be a differentiable function of x. Use the fact that
> Show that the derivative of an odd function is even. That is, if (-x) = -f(x), then f’(-x) = f’(x). Show that the derivative of an even function is odd. That is, if (-x) = -f(x), then f’(-x) = f’(x).
> Find the derivative of the function g(x) = sin2 x + cos2 x in two ways. For f(x) = sec2 x and g(x) = tan2 x, show that f’(x) = g’(x).
> Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find (a) r’(1) and (b) s’(4).
> Let f be a differentiable function of period p. Is the function f′ periodic? Verify your answer. Consider the function g(x) = f(2x). Is the function g′(x) periodic? Verify your answer.
> Find the derivative of the function. g(x) = 3(4 – 9x)5/6
> Consider the function f(x) = sin βx, where β is a constant. Find the first-, second-, third-, and fourth-order derivatives of the function. Verify that the function and its second derivative satisfy the equation f″(x) + β2 f(x) = 0. Use the results of pa
> The value V of a machine t years after it is purchased is inversely proportional to the square root of t + 1. The initial value of the machine is $10,000. Write V as a function of t. Find the rate of depreciation when t = 1. Find the rate of depreciation
> The number N of bacteria in a culture after t days is modeled by Find the rate of change of N with respect to t when t = 0, (b) t = 1, (c) t = 2, (d) t = 3, and (e) t = 4. (f) what can you conclude?
> The cost C (in dollars) of producing x units of a product is C = 60x + 1350. For one week, management determined that the number of units produced x at the end of t hours can be modeled by x = -1.6t3 + 19t2 – 0.5 t – 1
> The normal daily maximum temperatures T (in degrees Fahrenheit) for Chicago, Illinois, are shown in the table. Use a graphing utility to plot the data and find a model for the data of the form T(t) = a + b sin(ct - d) where T is the temperature and t is
> A buoy oscillates in simple harmonic motion y = A cos ωt as waves move past it. The buoy moves a total of 3.5 feet (vertically) from its low point to its high point. It returns to its high point every 10 seconds. Write an equation describing the motion o
> A 15-centimeter pendulum moves according to the equation θ = 0.2 cos 8t, where θ is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of θ when t = 3 seco
> The displacement from equilibrium of an object in harmonic motion on the end of a spring is /
> The frequency F of a fire truck siren heard by a stationary observer is Where ±v represents the velocity of the accelerating fire truck in meters per second. Find the rate of change of F with respect to v when The fire truck is approaching
> The graphs of f and g are shown. Let h(x) = f (g(x)) and s(x) = g( f (x)). Find each derivative, if it exists. If the derivative does not exist, explain why. Find h’ (3) Find s’ (9)
> y = 5(2 – x3)4 Find the derivative of the function.
> Describe the Chain Rule for the composition of two differentiable functions in your own words.
> Tawana owns and operates a sole proprietorship and has a 37 percent marginal tax rate. She provides her son, Jonathon, $8,000 a year for college expenses. Jonathon works as a pizza delivery person every fall and has a marginal tax rate of 15 percent. a)
> Cloud computing is the use of hosted computer facilities through the Internet. Gmail, RIA Checkpoint, and even your iPhone are some applications of cloud computing. a) If HP provides a customized bundle of servers, storage, network and security software,
> Winkin, Blinkin, and Nod are equal shareholders in SleepEZ, an S corporation. In the conditions listed below, how much income should each report from SleepEZ for 2019 under both the daily allocation and the specific identification allocation method? Refe
> Owl Vision Corporation (OVC) is a North Carolina corporation engaged in the manufacture and sale of contact lenses and other optical equipment. The company handles its export sales through sales branches in Belgium and Singapore. The average tax book val
> Sandra would like to organize BAL as either an LLC (taxed as a sole proprietorship) or a C corporation. In either form, the entity is expected to generate an 8 percent annual before-tax return on a $500,000 investment. Sandra’s marginal income tax rate i
> Spartan Corporation, a U.S. corporation, reported $2 million of pretax income from its business operations in Spartania, which were conducted through a foreign branch. Spartania taxes branch income at 15 percent, and the United States taxes corporate inc
