# How do you find the derivative of #(e^x)^2#?

##### 3 Answers

#### Explanation:

Use the exponent rule

Use

Let

#### Explanation:

#color(blue)"Note that " (e^x)^2=e^(2x)# differentiate using the

#color(blue)"chain rule"#

#• d/dx(e^(f(x)))=e^(f(x))xxf'(x)#

#rArrd/dx(e^(2x))=e^(2x)xxd/dx(2x)#

#color(white)(xxxxxxxx)=2e^(2x)#

For the heck of it, we can also treat

Generally, we see that the derivative of

The previous relation comes from the chain rule. The derivative of

Here, we see that the derivative of **then multiplied by the derivative of**

The derivative of

Which we can simplify using the rules of exponents: