By Christopher Thomas

Updated on Oct 1, 2011

To review these concepts, go to Implicit Differentiation Study Guide.

**Implicit Differentiation Practice Questions**

**Find in the following equations.**

- (
*y*+ 1)^{3}=*x*^{4}– 8*x* *y*^{3}+*y*= sin(*x**)*- sin(
*y*) = 4*x*+ 7 *y*– √*y*= ln(*x*)*y*^{2}+*x*= 3*x*^{4}+ 8*y**e*+^{x}*e*=^{y}*x*^{3}- tan(
*y*) = cos(*x*) *y*= √*x*+*y*- sin(
*x*) – sin(*y*) =*x* *y*– ln(*y*) = 10*x*^{3}– 6*x*^{2}+ 4- (
*y*+*x*^{2})^{4}= 10*x* *x*^{2}*y*=*y*^{4}*x*^{4}- +
*xy*=*x*+*y* - sec(
*y*) + 9*y*=*x*^{3}cos(*y*) - Find the tangent line slope of
*y*^{3}+*x*^{2}=*y*^{2}– 5*y*+ 14 at (–3, 1). - Find the tangent line slope of
*x*^{3}+*y*^{3}= 3*y*–*x*at (**1**, –2). - Find the slope of the tangent line to ln(3
*y*– 5) +*x*=*y*^{2}at (4,2). - Find the slope of the tangent line at (2,3) on the graph of
*x*^{2}*y*+*y*^{2}*x*= 30. - Find the equation of the tangent line to sin(
*y*) =*x*at the point . - Find the equation of the tangent line to
*x*^{2}+ 6*y*=*xy*+ 3 at (3, –2).

**Solutions**

- 3(
*y*+ 1)^{2}· = 4*x*^{3}– 8, so = - 3
*y*^{2}· + = cos(*x*), so = - = = 4sec(
*y*) - = =
- =
- =
- = = –sin(
*x*)cos^{2}(*y*) - = (1 + ), so = =
- =
- = =
- = – 2
*x* - =
- +
*y*+ ·*x*= 1 + , so = = - 3
*y*^{2}· + 2x = 2*y*· – 5 · , so at (–3,1), the tangent slope is = 1. - = – at (1,–2)
- = 1 at (4,2)
- = – at (2,3)
- = at (,), so the tangent equation is
*y*= (*x*– ) + . - = – at (3, –2) , so the tangent equation is
*y*= –(*x*– 3)– 2 = –*x*+ 6.

From Calculus Success in 20 Minutes A Day. Copyright © 2006 by LearningExpress, LLC. All Rights Reserved.

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