# What is the derivative of #sin^2 (5x)#?

##### 1 Answer

Mar 7, 2018

f'(x) = (10sin(5x))(cos(5x))

#### Explanation:

Let

1: Bring the square (2) outside of the brackets of the whole term.

f(x) =

f(x) =

2: Use chain rule by bringing the square to the front of the term and subtracting 1 from 2 outside of the brackets.

f(x) =

3: Determine the derivative of the term on the inside, sin(5x) and multiply it to the rest of the function.

f(x) =

*The derivative of sin(5x) is 5cos(5x). Bring your k value (5) to the front and leave the original the same.

4: Simplify. Multiply

f'(x) =