Derivatives of the Natural Exponential and Logarithmic Functions

MATH 11012

Intuitive Calculus

KSU

Worksheet: Derivatives of the Natural Exponential and Logarithmic Functions Compute each derivative using the short-cuts. 1.

d x (e ) = dx

2.

d e (x ) = dx

3.

d (5 ex ) = dx

9.

d ex dx x7 



=

d 2 ex − 1 10. = dx 5 ex + 9 

d (−ex ) = 4. dx



1 d ex + x10 − = 5. dx x 

6.

7.

8.



 d √ x − 600ex = dx

11.

d  2x  = e dx

12.

d  −x  e = dx

13.

d  x5 +3  e = dx

d (x ex ) = dx

 d  x 2 e x −7 = dx

d 1 14. dx ex 



=

d (ln x) = 15. dx 16.

d (12 ln x) = dx

17.

d (− ln x) = dx

18.

d 2 0.5 ln x − 3x25 − 3 dx x

19.

20.

21.





 i d h (ln x) x5 + 10x2 − 19 = dx

!

=

24.

d (ln (3x)) = dx

25.

d (ln (−x)) = dx

26.

d   2  ln x = dx

27.

 d   2 ln 2x − 1 = dx

 d  2 x ln x = dx

ln x x20

!

=

 d  0.5 4x − 8 ln x = dx

d 22. dx

2 ln x + 4 ln x − 1

d 23. dx

1 d 28. = dx ln x 



=

29.

d (ln (ex )) = dx

30.

d  ln x  e = dx