anonymous one year ago find f'(x) of f(x)=sin(2x)(sqrt(1+cos(5x)))

1. misty1212

HI!!

2. misty1212

product plus chain rule $(fg)'=f'g+g'f$ with $f(x)=\sin(x), f'(x)=\cos(x), g(x)=\sqrt{1+\cos(5x)}$ $g'(x)=\frac{-5\sin(5x)}{2\sqrt{1+\cos(5x)}}$

3. anonymous

what happened to the 2x inside sin(x)?

4. misty1212

oops $f(x)=\sin(2x), f'(x)=2\cos(2x)$ my bad

5. anonymous

How would I apply the chain rule to that? The sqrt makes it pretty messy.

6. anonymous

@misty1212 ?

7. misty1212

$\left(\sqrt{f}\right)'=\frac{f'}{2\sqrt{f}}$

8. misty1212

which should explain $g'(x)=\frac{-5\sin(5x)}{2\sqrt{1+\cos(5x)}}$

9. anonymous

That makes sense. I'm just not sure what to do from there. From the product rule I got 2cos(2x)(sqrt(1+cos(5x)))+sin(2x)((-5sin(5x))/2(sqrt(1+cos(5x))))

10. misty1212

leave it

11. anonymous

12. misty1212

it is a silly made up question anyway what else can you do?

13. misty1212

you sure as hell don't want to actually add them although you could if you had like an extra half hour to waste

14. anonymous

Haha definitely not. Still got 6 more questions on this homework sheet due tomorrow.

15. misty1212

best get busy

16. misty1212

lol not that "get busy"