Question

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

Answer 1

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

Explanation:

Let `sin^2(5x)` be f(x)
1: Bring the square (2) outside of the brackets of the whole term.

f(x) = `sin^2(5x)`
f(x) = `(sin(5x))^2`

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) = `(2sin(5x))^(2-1)`

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

f(x) = `(2sin(5x))(5cos(5x))`

*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) = `(10sin(5x))(cos(5x))`