# Homework Help: Differentiating a trig function to the power of 2

1. Aug 12, 2011

### chung963

1. The problem statement, all variables and given/known data
I'm doing a optimisation question and I get to a point where I have to verify a maximum using a double derivative and I need to differentiate -5sin^2(x)

2. Relevant equations
-5sin^2(x)

3. The attempt at a solution
-10cos(x)sin(x) im not sure if the answer is positive or negative.

2. Aug 12, 2011

### cragar

-10cos(x)sin(x) would be your first derivative .

3. Aug 12, 2011

### HallsofIvy

You are using the chain rule: $-5sin^2(x)$ can be written as $-5u^2$ with $u= sin(x)$. The derivative of $-5u^2$, with respect to u, is -10u and the derivative of $u= sin(x)$ with respect to x is $cos(x)$. Multiply those together.

4. Aug 12, 2011

### shiva999

it is negative and in order to find maximum value you have to differentiate once more