Question

what is the derivative of "e" to exponent sinx

Answer 1

do you know the chain rule?

Answer 2

let\[f(x)=\sin x\]we can then write this as\[\large e^{f(x)}\]so the derivative of this is\[\large e^{f(x)}f'(x)\]

Answer 3

what are the other laws linked to this specific one

Answer 4

you need to know three things:

1) the derivative of \(\sin x\) with respect to x
2) the derivative of \(e^x\) with respect to x
3) the chain rule: \(\large{du\over dx}={du\over dv}{dv\over dx}\)

Answer 5

let \(u=e^x\) and \(v=\sin x\)
then use the chain rule to get the result above

Answer 6

ok. so what is the derivative of 3 to exponent "X squared"