# Math Help - Derivative problem

1. ## Derivative problem

Hello, I have the following expression I'd like to derive in terms of 'x'. 'k' is just a constant.

$
f(x) = 2(\frac{\sin{x}+1}{2})^k
$

I haven't done this sort of maths for a while, any pointers?

2. Hello,

$f(x)=2(u(x))^k$

The derivative of such a function is :

$f'(x)=2ku'(x)(u(x))^{k-1}$

$u(x)=\frac{\sin(x)+1}{2}=\frac{\sin(x)}{2}+\frac{1 }{2}$

So $u'(x)=\frac{\cos(x)}{2}$

And then substitute it in f'(x)

3. Ah, great! Thanks.

This is what I got:

$
f'(x) = k\cos{x}\Bigl(\frac{\sin{x}+1}{2}\Bigr)^{k-1}
$

Is it correct?

4. Yes it is ^^

(hoping that k is different from 0)