# Math Help - Calculus Derivative HELP! Please

1. ## Calculus Derivative HELP! Please

Can some one help explain this to me i think i am suppose to the quotient rule to solve this.
Consider the function h(x), for which h(4)=4 and h(prime)(4)=(-4) or the derivative of h^1(4)=(-4)
Find F^1(4) for the function f(x)=(h(x))/(x)
Hopefully i explained that right
Thanks to anyone who can help
AC

2. Hello, Casas4!

By the way, the derivative is written: $f'(x)$ ... " $f$ prime" ... not $f^1$

Consider the function $h(x)$, for which $h(4)=4$ and $h'(4)= \text{-}4$

Find $f'(4)$ where: $f(x)\:=\:\frac{h(x)}{x}$

We are given: . $f(x) \:=\:\frac{h(x)}{x}$

Quotient Rule: . $f'(x) \;=\;\frac{x\!\cdot\!h'(x) - h(x)}{x^2}$

Therefore: . $f'(4) \;=\;\frac{4\!\cdot\!h'(4) - h(4)}{4^2} \;=\;\frac{4(\text{-}4) - 4}{16} \;=\;\frac{\text{-}20}{16} \;=\;\boxed{-\frac{5}{4}}$