Question

Find the derivative for the following:
a. y = x^2 e^x
b. y = (e^x + 2)^3/2
c. y = e^-3x
d. y = (e^x-e^-x)/2

Answer 1

a) (product rule)
y' = x^2 e^x + 2x e^x
= x e^x( x +2)

b) (chain rule)
y' = (3/2)(e^x + 2)^(1/2) (e^x)
= (3/2) e^x (e^x + 2)^(1/2)

c) y' = -3 e^(-3x)

d)
y = (1/2) e^x - (1/2) e^-x

y' = .....
give it a try, it is straightforward from here