Differentiation, please help!

[Estjohn79]

If h(2)=7 and h'(2)=-2 find f'(2) if f(x)=(h(x))/x.

 

[pka]

If h(2)=7 and h'(2)=-2 find f'(2) if f(x)=(h(x))/x.

If f(x)=(h(x))/x then \(\displaystyle f'(x)=\dfrac{x\cdot h'(x)-h(x)}{x^2}\) .

 

[stapel]

If h(2)=7 and h'(2)=-2 find f'(2) if f(x)=(h(x))/x.

To expand a smidge upon the previous reply, to find the derivative of f(x) = h(x)/x, apply the Quotient Rule:

. . . . .\(\displaystyle f'(x)\, =\, \dfrac{\frac{dh(x)}{dx}\cdot x\, -\, h(x)\cdot \frac{dx}{dx}}{(x)^2}\, =\, \dfrac{x\,h'(x)\, -\, h(x)}{x^2}\)

Then evaluate by plugging in the given values.