Hey can anyone help me with the following question....
use the composite rule to differentiate f(x) = e^cosx+sinx
thank you
composite rule is another name for chain rule isn't it?
differentiate the seperate terms
so $\displaystyle e^{cos(x)}$ diff's to $\displaystyle -sin(x)(e^{cos(x)})$ using the chain rule (or composite rule (i.e. you diff the first term, then multiply by the diff of term inside brackets)) and $\displaystyle sin(x)$ diff's to $\displaystyle cos(x)$ using standard rules. then just add them together at the end
$\displaystyle f'(x)=-sin(e^{cos(x)})+cos(x)$ and to be more artistic you would swap them so you don't start with a negative sign.
The derivative of $\displaystyle e^{cos(x)}$ is -sin(x) times $\displaystyle e^{cos(x)}$, not -sin of $\displaystyle e^{cos(x)}$ as you write.
using the chain rule (or composite rule (i.e. you diff the first term, then multiply by the diff of term inside brackets)) and $\displaystyle sin(x)$ diff's to $\displaystyle cos(x)$ using standard rules. then just add them together at the end
$\displaystyle f'(x)=-sin(e^{cos(x)})+cos(x)$ and to be more artistic you would swap them so you don't start with a negative sign.