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Section 3.1. 1. Implicitly differentiate to find dy/dx. y 3 – x 2 = 4. 2. Implicitly differentiate to find dy/dx. y 4 – x 3 = 2x. 3. Implicitly differentiate to find dy/dx. x 2 y = 8. Use the product rule. 4. Implicitly differentiate to find dy/dx. x(y – 1 ) 2 = 6.

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slide1

Section 3.1

1. Implicitly differentiate to find dy/dx.

y 3 – x 2 = 4

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3. Implicitly differentiate to find dy/dx.

x 2y = 8

Use the product rule.

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4. Implicitly differentiate to find dy/dx.

x(y – 1) 2 = 6

Use the product rule.

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5. Implicitly differentiate to find dy/dx.

Rewrite the original equation.

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6. Implicitly differentiate to find dy/dx and evaluate it at the given point.

y 2 – x 3 = 1 at x = 2, y = 3.

At x = 2, y = 3.

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7. Implicitly differentiate to find dy/dx and evaluate it at the given point.

x 2 y + y 2x = 0 at x = - 2, y = 2.

Use the product rule - twice.

At x = - 2, y = 2.

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8. For the following demand equation Implicitly differentiate to find dp/dx.

p 2 + p + 2x = 100

You are taking a derivative with respect to x, so a p term will have a dp/dx while an x term will have a dx/dx = 1.

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9. For the following demand equation Implicitly differentiate to find dp/dx.

xp 3 = 36

You are taking a derivative with respect to x, so a p term will have a dp/dx while an x term will have a dx/dx = 1. You also need to use the product rule.

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