Differentiating a trig function to the power of 2

[chung963]

Homework Statement

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)

Homework Equations

-5sin^2(x)

The Attempt at a Solution

-10cos(x)sin(x) I am not sure if the answer is positive or negative.

 

[cragar]

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

 

[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.

 

[shiva999]

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