Hey can anyone help me with the following question....

use the composite rule to differentiate f(x) = e^cosx+sinx

thank you

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- Jun 3rd 2009, 05:08 AMemmalou264help with composite rule question
Hey can anyone help me with the following question....

use the composite rule to differentiate f(x) = e^cosx+sinx

thank you - Jun 3rd 2009, 05:25 AMRapid_W
composite rule is another name for chain rule isn't it?

differentiate the seperate terms

so diff's to using the chain rule (or composite rule (i.e. you diff the first term, then multiply by the diff of term inside brackets)) and diff's to using standard rules. then just add them together at the end

and to be more artistic you would swap them so you don't start with a negative sign. - Jun 3rd 2009, 06:01 AMAmer
if you mean

- Jun 3rd 2009, 06:12 AMRapid_W
Yup, take your pick depending on what your question is :p

- Jun 3rd 2009, 06:49 AMemmalou264
well using the product rule of

k'(x)= f'(x)g(x) + f(x) g'(x)

and the previous equation, can i show the derivitave of the function

g(x) = (cosx + sinx - 1) e^cosx+sinx

is g'(x) = (cos^2x - sin^2x)e^cosx +sinx - Jun 3rd 2009, 07:03 AMHallsofIvy
The derivative of is -sin(x)

**times**, not -sin**of**as you write.

Quote:

using the chain rule (or composite rule (i.e. you diff the first term, then multiply by the diff of term inside brackets)) and diff's to using standard rules. then just add them together at the end

and to be more artistic you would swap them so you don't start with a negative sign.

- Jun 3rd 2009, 08:09 AMRapid_W
oops, missed the x out, simple error, have fixed my original post, thanks for pointing that out.