# How do you find the derivative of #f (x) = x^6 · e^(7x)#?

##### 1 Answer

Jan 21, 2016

#### Explanation:

Use the product rule, which states that for a function

#f'(x)=g'(x)h(x)+g(x)h'(x)#

We have:

#g(x)=x^6#

#h(x)=e^(7x)#

Find the derivatives of either function.

Through the power rule,

#g'(x)=6x^5#

Through the chain rule, particularly applied to

#h'(x)=e^(7x)d/dx[7x]=7e^(7x)#

Plug both of these into the original equation.

#f'(x)=6x^5e^(7x)+x^6(7e^(7x))#

#f'(x)=x^5e^(7x)(7x+6)#