Question

PRACTICE PROBLEM SET 7 Use implicit differentiation to find the following derivatives. 1. Find dy/dx if x^3 - y^3 = y. 2. Find dy/dx if x^2 - 16xy + y^2 = 1. 3. Find dy/dx at (2, 1) if (x + y)/(x - y) = 3. 4. Find dy/dx if 16x^2 - 16xy + y^2 = 1 at (1, 1). 5. Find dy/dx if x sin y + y sin x = ??/2?2 at (??/4, ??/4). 6. Find d^2y/dx^2 if x^2 + 4y^2 = 1. 7. Find d^2y/dx^2 if sin x + 1 = cos y. 8. Find d^2y/dx^2 if x^2 - 4x = 2y - 2.

          PRACTICE PROBLEM SET 7
Use implicit differentiation to find the following derivatives.

1. Find dy/dx if x^3 - y^3 = y.
2. Find dy/dx if x^2 - 16xy + y^2 = 1.
3. Find dy/dx at (2, 1) if (x + y)/(x - y) = 3.
4. Find dy/dx if 16x^2 - 16xy + y^2 = 1 at (1, 1).
5. Find dy/dx if x sin y + y sin x = ??/2?2 at (??/4, ??/4).
6. Find d^2y/dx^2 if x^2 + 4y^2 = 1.
7. Find d^2y/dx^2 if sin x + 1 = cos y.
8. Find d^2y/dx^2 if x^2 - 4x = 2y - 2.

PRACTICE PROBLEM SET 7
Use implicit differentiation to find the following derivatives.

1. Find dy/dx if x^3 - y^3 = y.
2. Find dy/dx if x^2 - 16xy + y^2 = 1.
3. Find dy/dx at (2, 1) if (x + y)/(x - y) = 3.
4. Find dy/dx if 16x^2 - 16xy + y^2 = 1 at (1, 1).
5. Find dy/dx if x sin y + y sin x = ??/2?2 at (??/4, ??/4).
6. Find d^2y/dx^2 if x^2 + 4y^2 = 1.
7. Find d^2y/dx^2 if sin x + 1 = cos y.
8. Find d^2y/dx^2 if x^2 - 4x = 2y - 2.

Added by Aaron W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/14/2023

Step 1

Find $\frac{dy}{dx}$ if $x^2 - y^2 = y$. We have the equation $x^2 - y^2 = y$. Differentiating both sides with respect to $x$, we get: $$2x - 2y\frac{dy}{dx} = \frac{dy}{dx}$$ Now, solve for $\frac{dy}{dx}$: $$\frac{dy}{dx} = \frac{2x}{2y - 1}$$ So, the answer Show more…

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