What is the derivative of f(x)= x^(4/5) (x-5)^2?

May 6, 2018

$f ' \left(x\right) = \frac{14}{5} {x}^{\frac{9}{5}} - 18 {x}^{\frac{4}{5}} + 20 {x}^{- \frac{1}{5}}$

Explanation:

$\text{differentiate using the "color(blue)"power rule}$

•color(white)(x)d/dx(ax^n)=nax^(n-1)

$\text{expand and distribute}$

$f \left(x\right) = {x}^{\frac{4}{5}} \left({x}^{2} - 10 x + 25\right)$

$\textcolor{w h i t e}{f \left(x\right)} = {x}^{\frac{14}{5}} - 10 {x}^{\frac{9}{5}} + 25 {x}^{\frac{4}{5}}$

$\Rightarrow f ' \left(x\right) = \frac{14}{5} {x}^{\frac{9}{5}} - 18 {x}^{\frac{4}{5}} + 20 {x}^{- \frac{1}{5}}$