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

Exponential functions - differentiation.
Test Yourself 2.


 

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

(follow this hyperlink for differential equations with exponentials).

Basic expressions. 1. y = e-2x 2. y = 1 + e3x
  3. y = 4e. 4.
  5. 6. .
  7. 8. Given that y = Ae-mt, where A and m are constants, show that

Chain rule. 9. y = (ex - 3)4 10.
  11. 12.
Product rule. 13. y = 4xe2x 14. y = (3x - 1)e-x
  15. If f(x) = (1 + 2x)e3x,

find f '(2) and f "(0).

Answer.f '(2) = 17e6
f "(0) = 21.		 16.
Quotient rule. 17. 18.
     
Tangents. 21. Find where the tangent to
y = e3x at the point (1, e3) cuts the x-axis.

22. Show that the tangent to the curve y = ex - 2x at the point
(1, e - 2) passes through the origin.
     
     
Normals. 27. Find the equation of the normal to the curve y = e4x - 1 at the point on the curve where x = 0.
Answer.Normal is x + 4y = 0.		  
    30.
Miscellaneous.

31.

32. If prove that

y' = 2y(2x2 - 3).