Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Exponential functions - differentiation.
Test Yourself 2 - Solutions.


 

Differentiate each of the following equations unless there is another instruction:

(follow this hyperlink for differential equations with exponentials).

Basic expressions 1. y' = -2e-2x 2. y = 1 + e3x

y' = 3e3x
  3. 4.
  5. 6.
  7. 8.
Chain rule

9. y = (ex - 3)4

y' = 4(ex - 3)3×ex

=4ex(ex - 3)3

 10.
  11. 12.
Product rule. 13. 14.
 

15.

16.

Quotient rule.

17.

You do not have to factorise as in the last step. It really depends on what you need to do next - in this case we need nothing more.
It does however look nicer :-)

 18.
     
Tangents 21.

22. Show that the tangent to the curve

y = ex - 2x

at the point (1, e - 2) passes through the origin.
  23.  
  25.  
Normals 27.  
  29.  
Miscellaneous.

31.

 32.