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

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

#### Explanation:

Let ${\sin}^{2} \left(5 x\right)$ be f(x)
1: Bring the square (2) outside of the brackets of the whole term.

f(x) = ${\sin}^{2} \left(5 x\right)$
f(x) = ${\left(\sin \left(5 x\right)\right)}^{2}$

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) = ${\left(2 \sin \left(5 x\right)\right)}^{2 - 1}$

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

f(x) = $\left(2 \sin \left(5 x\right)\right) \left(5 \cos \left(5 x\right)\right)$

*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) = $\left(10 \sin \left(5 x\right)\right) \left(\cos \left(5 x\right)\right)$