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# Implicit Differentiation Practice Questions

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Updated on Oct 1, 2011

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

## Implicit Differentiation Practice Questions

Find in the following equations.

1. (y + 1)3 = x4 – 8x
2. y3 + y = sin(x)
3. sin(y) = 4x + 7
4. y – √y = ln(x)
5. y2 + x = 3x4 + 8y
6. ex + ey = x3
7. tan(y) = cos(x)
8. y = √x + y
9. sin(x) – sin(y) = x
10. y – ln(y) = 10x3 – 6x2 + 4
11. (y + x2)4 = 10x
12. x2y = y4x4
13. + xy = x + y
14. sec(y) + 9y = x3 cos(y)
15. Find the tangent line slope of y3 + x2 = y2 – 5y + 14 at (–3, 1).
16. Find the tangent line slope of x3 + y3 = 3yx at (1, –2).
17. Find the slope of the tangent line to ln(3y – 5) + x = y2 at (4,2).
18. Find the slope of the tangent line at (2,3) on the graph of x2y + y2x = 30.
19. Find the equation of the tangent line to sin(y) = x at the point .
20. Find the equation of the tangent line to x2 + 6y = xy + 3 at (3, –2).

### Solutions

1. 3(y + 1)2 · = 4x3 – 8, so =
2. 3y2 · + = cos(x), so =
3. = = 4sec(y)
4. = =
5. =
6. =
7. = = –sin(x)cos2(y)
8. = (1 + ), so = =
9. =
10. = =
11. = – 2x
12. =
13. + y + · x = 1 + , so = =
14. 3y2 · + 2x = 2y · – 5 · , so at (–3,1), the tangent slope is = 1.
15. = – at (1,–2)
16. = 1 at (4,2)
17. = – at (2,3)
18. = at (,), so the tangent equation is y = (x) + .
19. = – at (3, –2) , so the tangent equation is y = –(x – 3)– 2 = – x + 6.

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