Directions: In implicit differentiation, we differentiate each side of an equation with twovariables (usually xxx and yyy) by treating one of the variables as a function of the other. Thiscalls for using the chain rule.2x³y+ 3xy3 = 510. x = sin (x + y)%3D9.

Answered: Image /qna-images/answer/01ff3e55-dc23-40a3-9db0-5d9818bf3487.jpg

Answered: Directions: In implicit…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(a) If f(x) = ln(cos 2x) then find the slope of the graph of f(x) at x = π/8.(b) Find the equation of the tangent line to the graph of the equation−x^2y-3xy^2+y^3=-4at the point (1, 2)
a. Use implicit differentiation to find dy/dx. b. Find the slope of the curve at the given point. 7xy=5; (1, 5/7)
f'(x)= limh->0 (cos (h)-1)/h this represents the derivative of a function f(x) at a number x=a, find f(x) and the number a.
differntiate y=ax^2 +bx+r Find an equation for the tangent line to the curve at the given point (2,2) y=4x/x+2 Differntiate f(x)= 8x^7 -4 cos(x)
2.6 Can you show me the steps to solve the problem? Directions: Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy. 23) x4y2 - x3y + 2xy3 = 0
Find the values of h, k, and a that make the circle (x - h)2 + (y - k)2 = a2 tangent to the parabola y = x2 + 1 at the point (1, 2) and that also make the second derivatives d2y/dx2 have the same value on both curves there. Circles like this one that are tangent to a curve and have the same second derivative as the curve at the point of tangency are called osculating circles.
Using the points given below, calculate the value of f (1.5) using a cubic spline, instead of accepting second derivatives as zero for only the first and last points as in the standard case, Consider the first derivatives zero.
P(x)= sin^-1(f(x)) what is the derivative of p at 2 I(x)=f(f(x)) what is the derivative of i at -1 Y(x)= sin(3pif(x)) what is the derivative of y at 0
Experiment 1: 1D. State the slope of the tangent line by substituting x = 2 into the derivative f'(x). State the value f'(2). 1E. Does f'(2), the y-coordinate on the gray line at x = 2, have any relationship to the derivative value f'(2)? 1F. Does f'(2), the y-coordinate on the gray line at x = 2, have any relationship to f(2), the y-coordinate on the parabola at x = 2?
Experiment 3: 3D. Does f'(0), the y-coordinate on the gray line at x = 0, have any relationship to the derivative value f'(0)? 3E. Does f'(0), the y-coordinate on the derivative line at x = 0, have any relationship to f(0), the y-coord. on the parabola at x = 0?
Using implicit differentiation, find an equation of the tangent line to the curve at the given point a) y sin(8x) = x cos(2y), (pi/2, pi/4) b) x2+y2 = (2x2 + 4y2 -x)2, (0, 0.25)
(a) Use implicit differentiation to find y' if x2 +xy +y2 +1 = 0.(b) Plot the curve in part (a). What do you see? Prove thatwhat you see is correct.(c) In view of part (b), what can you say about the expressionfor y' that you found in part (a)?

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Directions: In implicit differentiation, we differentiate each side of an equation with wo variables (usually xxx and yyy) by treating one of the variables as a function of the other. This- calls for using the chain rule. 2x³y+ 3xy³ = 5 %3D 9. 10. x = sin (x + y)