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Kuta Software - Infinite Calculus Name___________________________________
Implicit Differentiation Date________________ Period____
dy
For each problem, use implicit differentiation to find in terms of x and y.
dx
1) 2x3 = 2y2 + 5 2) 3x2 + 3y2 = 2
3) 5y2 = 2x3 − 5y 4) 4x2 = 2y3 + 4y
5) 5x3 = −3xy + 2 6) 1 = 3x + 2x2y2
7) 3x2y2 = 4x2 − 4xy 8) 5x3 + xy2 = 5x3y3
3 ( )2 2 ( 2 3 )2
9) 2x = 3xy + 1 10) x = 4x y + 1
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11) sin 2x2y3 = 3x3 + 1 12) 3x2 + 3 = ln 5xy2
22
d22y
For each problem, use implicit differentiation to find 22 in terms of x and y.
dx22
13) 4y2 + 2 = 3x2 14) 5 = 4x2 + 5y2
Critical thinking question:
dy 3x2
15) Use three strategies to find 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?
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Kuta Software - Infinite Calculus Name___________________________________
Implicit Differentiation Date________________ Period____
dy
For each problem, use implicit differentiation to find in terms of x and y.
dx
1) 2x3 = 2y2 + 5 2) 3x2 + 3y2 = 2
dy 3x2 dy x
= = −
dx 2y dx y
3) 5y2 = 2x3 − 5y 4) 4x2 = 2y3 + 4y
dy 6x2 dy 4x
= =
dx 10y + 5 dx 3y2 + 2
5) 5x3 = −3xy + 2 6) 1 = 3x + 2x2y2
dy −y − 5x2 dy −3 − 4xy2
= =
dx x dx 4x2y
7) 3x2y2 = 4x2 − 4xy 8) 5x3 + xy2 = 5x3y3
dy 4x − 2y − 3xy2 dy 15x2y3 − 15x2 − y2
= =
dx 3x2y + 2x dx 2xy − 15x3y2
3 ( )2 2 ( 2 3 )2
9) 2x = 3xy + 1 10) x = 4x y + 1
dy −3y2x − y + x2 dy −32y6x2 − 8y3 + 1
= =
dx 3x2y + x dx 48x3y5 + 12xy2
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11) sin 2x2y3 = 3x3 + 1 12) 3x2 + 3 = ln 5xy2
dy 9x − 4y3cos 2x2y3 dy 6yx2 − y
= =
dx 6xy2cos 2x2y3 dx 2x
22
d22y
For each problem, use implicit differentiation to find 22 in terms of x and y.
dx22
13) 4y2 + 2 = 3x2 14) 5 = 4x2 + 5y2
d2y 12y2 − 9x2 d2y −20y2 − 16x2
= =
dx2 16y3 dx2 25y3
Critical thinking question:
dy 3x2
15) Use three strategies to find 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?
dy 6xy − 4y2 dy 6x − 4y dy 3
Strategy 1: = 2 , Strategy 2: = , Strategy 3: = To show all
dx 3x dx 4x dx 4
3x
answers are the same, plug y = into results for strategies 1 and 2.
4
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Infinite Calculus
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