# Math Help - derivative problem

1. ## derivative problem

If f(x)= (the fifth root of x^2) - (8/x) then f(x) = ?

I started by setting it up as follows
{x^(2/5)} - (8x^-1)
I then used the power rule to get:
{(2/5x)^(-3/5)}-(8x^-2) but that doesn't go through as correct. Can someone point out where I am going wrong?

Thanks

2. Originally Posted by juventinoalex
If f(x)= (the fifth root of x^2) - (8/x) then f(x) = ?

I started by setting it up as follows
{x^(2/5)} - (8x^-1)
I then used the power rule to get:
{(2/5x)^(-3/5)}-(8x^-2) but that doesn't go through as correct. Can someone point out where I am going wrong?

Thanks
$\displaystyle \frac{d}{dx}\left(\sqrt[5]{x^2} - \frac{8}{x}\right) = \frac{2}{5}x^{-\frac{3}{5}} + 8x^{-2} = \frac{2}{5\sqrt[5]{x^3}} + \frac{8}{x^2}$
5. Also you are using the power rule incorrectly. The derivative of $x^{2/5}$ is $(2/5)x^{-3/5}$, not $(2/5x)^{-3/5}$.