Kuta Software - Infinite Calculus
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Implicit Differentiation
Date________________ Period____
For each problem, use implicit differentiation to find
dy
in terms of x and y.
dx
1) 2 x 3 = 2 y 2 + 5
2) 3 x 2 + 3 y 2 = 2
3) 5 y 2 = 2 x 3 − 5 y
4) 4 x 2 = 2 y 3 + 4 y
5) 5 x 3 = −3 xy + 2
6) 1 = 3 x + 2 x 2 y 2
7) 3 x 2 y 2 = 4 x 2 − 4 xy
8) 5 x 3 + xy 2 = 5 x 3 y 3
9) 2 x 3 = (3 xy + 1) 2
10) x 2 = (4 x 2 y 3 + 1) 2
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Worksheet by Kuta Software LLC
11) sin 2 x 2 y 3 = 3 x 3 + 1
12) 3 x 2 + 3 = ln 5 xy 2
For each problem, use implicit differentiation to find
d 2y
in terms of x and y.
dx 2
13) 4 y 2 + 2 = 3 x 2
14) 5 = 4 x 2 + 5 y 2
Critical thinking question:
3x2
dy
in terms of x and y, where
= x. Strategy 1: Use implicit differentiation
dx
4y
directly on the given equation. Strategy 2: Multiply both sides of the given equation by the denominator of
the left side, then use implicit differentiation. Strategy 3: Solve for y, then differentiate. Do your three
answers look the same? If not, how can you show that they are all correct answers?
15) Use three strategies to find
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Worksheet by Kuta Software LLC