Question

find the derivative of f(x)=(2x^1/4-x^-1/4)^2

Answer 1

gsrttn do u know how to do this

Answer 2

Yes I know..

Answer 3

may you show me how step by step

Answer 4

\[\large \implies 2[2x^{\frac{1}{4}} - x^{\frac{-1}{4}}][2 \cdot \frac{1}{4} \cdot x^{\frac{-3}{4}} + \frac{1}{4} \cdot x^{\frac{-5}{4}}]\]

Can you simplify this by yourself...???

Answer 5

Do you know the power rule for derivative???

Answer 6

yes

Answer 7

are thore brackets supposed to be parenthesis

Answer 8

\[f(x)=(2x^{1/4}-x^{-1/4})^2\]\[\frac{df(x)}{dx}=2\left(2x^{1/4}-x^{-1/4}\right)\frac{d}{dx}\left(2x^{1/4}-x^{-1/4}\right)\]

Answer 9

\[\frac{df(x)}{dx}=2\left(2x^{1/4}-x^{-1/4}\right)\left(\frac{1}{2}x^{-3/4}+\frac{1}{4}x^{-5/4}\right)\]

Answer 10

and some easy but tedious algebra that I don't want to type out gets you to \[\frac{df}{dx}=\frac{4x-1}{2x^{3/2}
}\]