# What is the derivative of #y=3x^2e^(5x)# ?

##### 1 Answer

Jul 24, 2014

This is a product of the function

Thus we will need the product rule to the effect that:

#(3x^2 e^(5x))'=(3x^2)'e^(5x)+3x^2(e^(5x))'#

As well as the fact that:

#(3x^2)'=6x#

Using these basic differentiation rules, and the Chain Rule combined with

#(e^(5x))'=e^(5x)\times (5x)'=5e^(5x)# .

As a result:

#(3x^2 e^(5x))'=6xe^(5x)+15x^2e^(5x)# .