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Chapter 6

Implicit Differentiation

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Problem 1

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d y}{d x}$ if $x^{3}-y^{3}=y$

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Problem 2

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d y}{d x}$ if $x^{2}-16 x y+y^{2}=1$

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Problem 3

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d y}{d x}$ at $(2,1)$ if $\frac{x+y}{x-y}=3$

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Problem 4

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d y}{d x}$ if $16 x^{2}-16 x y+y^{2}=1$ at $(1,1)$

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Problem 5

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d y}{d x}$ if $x \sin y+y \sin x=\frac{\pi}{2 \sqrt{2}}$ at $\left(\frac{\pi}{4}, \frac{\pi}{4}\right)$

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Problem 6

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d^{2} y}{d x^{2}}$ if $x^{2}+4 y^{2}=1$

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Problem 7

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d^{2} y}{d x^{2}}$ if $\sin x+1=\cos y$

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Problem 8

Use implicit differentiation to find the following derivatives. The answers are in Chapter $19 .$
Find $\frac{d^{2} y}{d x^{2}}$ if $x^{2}-4 x=2 y-2$

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