Question

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

Answer 1

`f'(x)=14/5x^(9/5)-18x^(4/5)+20x^(-1/5)`

Explanation:

`"differentiate using the "color(blue)"power rule"`

`•color(white)(x)d/dx(ax^n)=nax^(n-1)`

`"expand and distribute"`

`f(x)=x^(4/5)(x^2-10x+25)`

`color(white)(f(x))=x^(14/5)-10x^(9/5)+25x^(4/5)`

`rArrf'(x)=14/5x^(9/5)-18x^(4/5)+20x^(-1/5)`