1. ## Another derivative

Hi,

I'm not sure what rules I'd use to solve down this derivative and how I'd go about employing these rules.

I need to find the derivative of:

$f(x)=(x^5-3x)(\frac{1}{x^2})$

If you can guide me that would be excellent. Thank you.

2. If $f(x)=x^n$
$f'(x)=nx^{n-1}$

$f(x)=x^3-\frac{3}{x}$
$f'(x)=3x^2+\frac{3}{x^2}$

3. Originally Posted by jimmyp
Hi,

I'm not sure what rules I'd use to solve down this derivative and how I'd go about employing these rules.

I need to find the derivative of:

$f(x)=(x^5-3x)(\frac{1}{x^2})$

If you can guide me that would be excellent. Thank you.
You could use the product rule, but it's easier just to multiply out and use the power rule. like so:

$\frac{d}{dx}[(x^5-3x)(\frac{1}{x^2})]=\frac{d}{dx}[(x^{-2})(x^5-3x)]=\frac{d}{dx}[(x^{5+(-2)}-3x^{1+(-2)}]$

$=\frac{d}{dx}[x^{3}-3x^{-1}]=3x^{2}+3x^{-2}=3x^2+\frac{3}{x^2}$