Math Help - differentiate the trig function

1. differentiate the trig function

I need to differentiate this function:
secx^2-tanx^2+cosx. these are my steps:
f'(x)= secx^2*tanx^2-secx^2-sinx and do not know how to finish this but i know the first two terms are suppose to cancel. the answer is suppose to be -sin x.

And also, How does 2 sinx cosx translate to sin2x?

2. Originally Posted by driver327
I need to differentiate this function:
secx^2-tanx^2+cosx. these are my steps:
f'(x)= secx^2*tanx^2-secx^2-sinx and do not know how to finish this but i know the first two terms are suppose to cancel. the answer is suppose to be -sin x.
I dont know if this is right, please double check it.

$sec^2 x - tan^2 x + cos x$

$\frac{dy}{dx} = (2 sec x)(sec x \ tan x) - (2 tan x)( sec^2 x ) - (sin x)$

$= \frac{2 sin x}{cos^3 x} - \frac{2 sin x}{cos^3 x} - (sin x)$

$= - sin x$

3. Originally Posted by driver327

And also, How does 2 sinx cosx translate to sin2x?
That's a long proof. Please PM me about that. I need to find it somewhere in my book.

4. Originally Posted by driver327
How does 2 sinx cosx translate to sin2x?
Use the addition formula for sine.

$\sin 2x = \sin (x + x)$

$= \sin x \cos x + \sin x \cos x$

$= 2 \sin x \cos x$

5. Originally Posted by Jhevon
Use the addition formula for sine.

$\sin 2x = \sin (x + x)$

$= \sin x \cos x + \sin x \cos x$

$= 2 \sin x \cos x$
I thought he wanted the full proof...

In school we make use of Pythagoras and the distance formula to prove it.

6. Originally Posted by janvdl
I thought he wanted the full proof...

In school we make use of Pythagoras and the distance formula to prove it.
i don't think so. the question he asked was for a derivative, so i assume he wanted to know why someone would go between 2sin(x)cos(x) and sin(2x) to take a derivative (taking the derivative of the latter is much easier), so i didn't think a full proof was needed since it would just be an intermediate step for finding a derivative or something. besides, the wording he used kind of hinted he wasn't after a proof. he would more likely use the word "show" or "prove" or "proof" if he was after that

7. Just to clear the confusion, i just wanted to see how one trig function turns into another. Jhevon was right.