Question

Hey everybody im stuck on this problem
Find the derivative of 8/(2+3e^(-x/2))
could someone please help?

Answer 1

\[f(x)=\frac{8}{2+3e^{-x/2}}\]
I don't know about you, but I prefer avoiding using the quotient rule whenever possible. To that end, I'll rewrite
\[f(x)=8\left(2+3e^{-x/2}\right)^{-1}\]
Now apply the chain rule to differentiate:
\[f'(x)=-8\left(2+3e^{-x/2}\right)^{-2}\frac{d}{dx}\left[2+3e^{-x/2}\right]\]
Think you can do the rest?

Answer 2

What else do i need to do isnt that the derivative?

Answer 3

There's still the matter of taking the remaining derivative. Have you learned the chain rule yet?
\[f'(x)=-8\left(2+3e^{-x/2}\right)^{-2}\color{red}{\frac{d}{dx}\left[2+3e^{-x/2}\right]}\]