for f(x)=x*[1-4/(x+3)]
what would be the easier way to solve this?
put x into each equation then find derivative?
$\displaystyle f(x) = x\left(1 - \frac{4}{x + 3}\right)$
$\displaystyle = x\left[1 - 4(x + 3)^{-1}\right]$.
Now use the product rule.
$\displaystyle f'(x) = x\left[1 - 4(x + 3)^{-1}\right]' + \left[1 - 4(x + 3)^{-1}\right](x)'$
$\displaystyle = x \cdot 4(x + 3)^{-2} + \left[1 - 4(x + 3)^{-1}\right]\cdot 1$
$\displaystyle = \frac{4x}{(x + 3)^2} + 1 - \frac{4}{x + 3}$.