derivative problem

**juventinoalex** · September 25th 2010, 12:57 PM

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

**skeeter** · September 25th 2010, 01:09 PM

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

watch your signs ...

{(2/5x)^(-3/5)}+(8x^-2)

**juventinoalex** · September 25th 2010, 01:14 PM

OK, well actually I made a mistake here that I didn't there. I actually entered (2/5x)^(-3/5)+(8/x^-2) but that was wrong. Any other ideas. :-)

**skeeter** · September 25th 2010, 01:46 PM

Originally Posted by juventinoalex

OK, well actually I made a mistake here that I didn't there. I actually entered (2/5x)^(-3/5)+(8/x^-2) but that was wrong. Any other ideas. :-)

$\displaystyle \frac{d}{dx}\left(\sqrt[5]{x^2} - \frac{8}{x}\right) = \frac{2}{5}x^{-\frac{3}{5}} + 8x^{-2} = \frac{2}{5\sqrt[5]{x^3}} + \frac{8}{x^2}$