AP CALCULUS IMPLICIT DIFFERENTIATION PROBLEMS AND SOLUTIONS

In each case, find ᵈʸ⁄dₓ.

Problem 1 :

x² + y² = 25

Solution :

x² + y² = 25

Differentiate with respect to x.

Problem 2 :

4x³y² + 3x = 1

Solution :

4x³y² + 3x = 1

Differentiate with respect to x.

Problem 3 :

x²y² + 3xy + y = 0

Solution :

x²y² + 3xy + y = 0

Differentiate with respect to x.

Problem 4 :

ln (x + y) = 5x²

Solution :

ln (x + y) = 5x²

Differentiate with respect to x.

Problem 5 :

e^y = xy²

Solution :

e^y = xy²

Differentiate with respect to x.

Problem 6 :

sin(x² + y²) = e^y

Solution :

sin(x² + y²) = e^y

Differentiate with respect to x.

cos(x² + y²) ⋅ (x² + y²)' = e^y(y)'

Problem 7 :

3y² - cos y = x³

Solution :

3y² - cos y = x³

Differentiate with respect to x.

Problem 8 :

sin x = x(1 + tan y)

Solution :

sin x = x(1 + tan y)

sin x = x + xtan y

Differentiate with respect to x.

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