Paul's Online Math Notes
Calculus I (Assignment Problems) / Derivatives / Implicit Differentiation   [Notes] [Practice Problems] [Assignment Problems]

Calculus I - Assignment Problems
Limits Previous Chapter   Next Chapter Applications of Derivatives
Chain Rule Previous Section   Next Section Related Rates

 Implicit Differentiation

For problems 1  6 do each of the following.

(a)   Find  by solving the equation for y and differentiating directly.

(b)   Find  by implicit differentiation.

(c)    Check that the derivatives in (a) and (b) are the same.

 

1.  

 

2.  

 

3.  

 

4.  

 

5.  

 

6.  

 

For problems 7  21 find  by implicit differentiation.

 

7.  

 

8.  

 

9.  

 

10.  

 

11.  

 

12.  

 

13.  

 

14.  

 

15.  

 

16.  

 

17.  

 

18.  

 

19.  

 

20.  

 

21.  

 

For problems 22 - 24 find the equation of the tangent line at the given point.

 

22.  at  

 

23.  at  

 

24.  at  

 

For problems 25  27 determine if the function is increasing, decreasing or not changing at the given point.

 

25.  at  

 

26.  at  

 

27.  at  

 

For problems 28 - 31 assume that ,  and  and differentiate the given equation with respect to t.

 

28.  

 

29.  

 

30.  

 

31.  

 

Chain Rule Previous Section   Next Section Related Rates
Limits Previous Chapter   Next Chapter Applications of Derivatives

Calculus I (Assignment Problems) / Derivatives / Implicit Differentiation    [Notes] [Practice Problems] [Assignment Problems]

© 2003 - 2017 Paul Dawkins