MHB Derivatives of trigonometric equation

[Emjay]

Could I please get help with the following question?
f(x)=(2cos^2 x+3)^5/2

Any help would be very much appreciated:)

 

[MarkFL]

Hello, and welcome to MHB! (Wave)

Just to be clear, we are given:

$$f(x)=\left(2\cos^2(x)+3\right)^{\Large{\frac{5}{2}}}$$

And we are asked to compute $f'(x)$...correct?

If that's not correct, please let us know, but if it is...can you post what you've tried? This way we can see what you might be doing wrong. :)

 

[Emjay]

Yes, that is correct :)
Honestly, not even sure where to start with this one.
I have only ever done basic examples and this one has got me stumped.

 

[MarkFL]

Yes, that is correct :)
Honestly, not even sure where to start with this one.
I have only ever done basic examples and this one has got me stumped.

Okay, suppose we have:

$$g(x)=\left(h(x)\right)^r$$

The power and chain rules tell us:

$$g'(x)=r\left(h(x)\right)^{r-1}h'(x)$$

Using this formula, we can then write:

$$f'(x)=\frac{5}{2}\left(2\cos^2(x)+3\right)^{\Large{\frac{3}{2}}}\left(2\cos^2(x)+3\right)'$$

Can you proceed, using the formula again to compute the indicated differentiation?

 

[Emjay]

That helped heaps, thank you.
I do have a separate question to ask so i'll re post

Thanks again :)