Question

f(x) = e^-x · x^3 · tan(x)

What´s the derivative of the function?

I realise that I´ll be needing step-by-step instructions on how to solve this :)

Answer 1

Is this your function
\[
e^{-x} x^3 \tan(x)\]

Answer 2

Use the product rule
\[
(u v w)'=u'vw + uv'w +uvw'\]

Answer 3

\[

f'(x)=-e^{-x} x^3 \tan (x)+e^{-x} x^3 \sec ^2(x)+3 e^{-x} x^2 \tan (x)\]

Answer 4

Is it possible to simplify it?

Answer 5

to do that, you would need to add up like terms, which doesnt seem possible
you could always factor stuff out like the \[e^{-x}\]

Answer 6

ok