AP CALCULUS IMPLICIT DIFFERENTIATION PROBLEMS AND SOLUTIONS

In each case, find ᵈʸ⁄d.

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 :

ey = xy2

Solution :

ey = xy2

Differentiate with respect to x.

Problem 6 :

sin(x2 + y2) = ey

Solution :

sin(x2 + y2) = ey

Differentiate with respect to x.

cos(x2 + y2⋅ (x2 + y2)' = ey(y)'

Problem 7 :

3y- cos y = x3

Solution :

3y- 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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