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