Ive used the compsite rule to differentiate e^cosx to get -sinx(e^cosx) (hope i got that bit right)

I now need to use another rule and my answer to diferentiate:

(1-cosx)e^cosx

the answer i came up with was:

(-(-sinx)e^cosx)+((1-cosx)(-sinxe^cosx)) which i think is completely wrong, can anyone point me in the right direction please?

2. I think I might have worked it out however any comments would be greatly appreciated:

Using the Composite rule I differentiated e^cosx to get -sinxe^cosx

I would then use the product rule now to differentiate (1-cosx)e^cosx?

I know if h(x)=f(x)g(x)

f(x)=(1-cosx)
g(x)=e^cosx

f’(x)=-(-sinx)
g’(x)=-sinxe^cosx

So h’(x)=f’(x)g(x)+g’(x)f(x)

= (sinxe^cosx) + (-sinxe^cosx)(1-cosx)

= sinxe^cosx - sinxe^cosx + cosxsinxe^cosx

= cosxsinxe^cosx

Does this seem the right way of working it?

3. Originally Posted by turkish1066
e^cosx to get -sinx(e^cosx) (hope i got that bit right)
Right!

Originally Posted by turkish1066
I now need to use another rule and my answer to diferentiate:

(1-cosx)e^cosx
First $(1-\cos x)e^{\cos x}=e^{\cos x}-e^{\cos x}\cos x$

Now derive (use the product rule)