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

Question

anonymous · Answer

gsrttn do u know how to do this

anonymous · Answer

Yes I know..

anonymous · Answer

may you show me how step by step

anonymous · Answer

$$\large \implies 2[2x^{\frac{1}{4}} - x^{\frac{-1}{4}}][2 \cdot \frac{1}{4} \cdot x^{\frac{-3}{4}} + \frac{1}{4} \cdot x^{\frac{-5}{4}}]$$

Can you simplify this by yourself...???

anonymous · Answer

Do you know the power rule for derivative???

anonymous · Answer

yes

anonymous · Answer

are thore brackets supposed to be parenthesis

richyw · Answer

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

richyw · Answer

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

richyw · Answer

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