looking for help with trig function involving chain rule...

G

Guest

Guest
The question says to differentiate f'(4)...

Here's the function...

f(x) = (3sin5x)/(1+cosx)

Here's my work...

f'(x) = [(1+cosx)(15cos5x) - (3sin5x)(-sinx)] / (1+cosx)^2

f'(x) = [15cos5x + 15cos^2(5x) + 3sin^2(5x)] / (1+cosx)^2

f'(4) = [3(2.04 + .83 + .83)] / .12

f'(4) = 92.5

That's what I did, and the automative website says it's incorrect. I must be doing something wrong. Any help would be greatly appreciated.
 
(3sin5x)(-sinx) does not equal 3sin^2(5x) because the arguments for sine are different.

Whenever I am asked to evaluate a derivative at an arbitrary value, I plug in the value as soon as I can, unless simplification makes the calculation much easier. That way I can try to avoid careless errors like that one.
 
Ok, so I went ahead and fixed my mistake... and i'm still not getting the right answer...

i keep getting 38.5

any ideas?
 
f'(x) = [(1+cosx)(15cos5x) - (3sin5x)(-sinx)] / (1+cosx)^2

derivative is fine, I get f'(4) = .3948696718...

I see your mistake, 2nd line of your work.

15cos(5x)*cosx does not equal 15cos^2(5x)
 
Thank you so much. It's funny because that was my first answer, but I only used 2 decimal places so it told me I was wrong. Ha! Thanks!
 
Re: looking for help with trig function involving chain rule

bsalerno said:
The question says to differentiate f'(4)...
Click to expand...
The question should not say that. To differentiate f'(4), one should get zero (0).

If you mean:
1) Given f(x),
2) Differentiate to find f'(x), then
3) Evaluate f'(x) at x=4.
That is a different problem.
 
No, we didn't know. We assumed.

Let us, please, spend a little time writing clearly. Words mean things.
 
You must log in or register to reply here.
Top