Thread: composite / chain rule....differentiate

hi can someone lease help with the following question as i have done anythng this hard with the composite/chain rule

Q) use the composite rule to differentiate the function

f(x)= e^cos x+ sin x

thanx

is your equation $\displaystyle f(x) = e^{cos(x)}+sin(x)$ or $\displaystyle f(x) = e^{cos(x)+sin(x)}$ ?

either way you should employ the rule

$\displaystyle \frac{d}{dx}\left(e^{f(x)}\right) = f'(x)e^{f(x)}
$

its the second option ....

Originally Posted by redieeee_babieeee

its the second option ....

As pickslides said, what you need to do is:

$\displaystyle \frac{d}{dx}\left(e^{f(x)}\right) = f'(x)e^{f(x)}$

Can you differentiate $\displaystyle cos(x)+sin(x)$?

so can i just check that the anwser will be

-sin(x)+cos(x)

thanx

Originally Posted by redieeee_babieeee

so can i just check that the anwser will be

-sin(x)+cos(x)

thanx

Yep that's right, I'd write it with the $\displaystyle (\cos{x} - \sin{x})$ before the $\displaystyle e^{cos(x)+sin(x)}$ for clarities sake, but that's just me being pedantic

$\displaystyle f'(x) = (\cos{x} - \sin{x})e^{cos(x)+sin(x)}$