# Thread: What's the derivative of (1/3x^2)?

1. ## What's the derivative of (1/3x^2)?

What's the derivative of (1/3x^2)? I dont really understand how to use the power rule with this one. I know its Y'=Nx^N-1 but how do I put this fraction into something like that? Is it like 3x^-3? then taking the derivative of that becomes -9^-4???? The entire quiestion is (1/3x^-2) - (5/2x) I dont understand how to find the derivative of the other side either really. Help GREATLY appreciated.

2. Originally Posted by jmoh
What's the derivative of (1/3x^2)? I dont really understand how to use the power rule with this one. I know its Y'=Nx^N-1 but how do I put this fraction into something like that? Is it like 3x^-3? then taking the derivative of that becomes -9^-4???? The entire quiestion is (1/3x^-2) - (5/2x) I dont understand how to find the derivative of the other side either really. Help GREATLY appreciated.
$\displaystyle \frac{d}{dx} \left[\frac{1}{3x^2}\right]= \frac{1}{3}~\frac{d}{dx}\left[ \frac{1}{x^2}\right]=$$\displaystyle \frac{1}{3}~\frac{d}{dx} \left[ x^{-2} \right]$

Then apply the power rule to $\displaystyle x^{-2}$ with $\displaystyle N=-2$

RonL

3. Originally Posted by jmoh
What's the derivative of (1/3x^2)? I dont really understand how to use the power rule with this one. I know its Y'=Nx^N-1 but how do I put this fraction into something like that? Is it like 3x^-3? then taking the derivative of that becomes -9^-4???? The entire quiestion is (1/3x^-2) - (5/2x) I dont understand how to find the derivative of the other side either really. Help GREATLY appreciated.
$\displaystyle y=\frac{1}{3x^2} = \frac{1}{3}x^{-2}$

$\displaystyle \implies y' = \frac{1}{3} \cdot (-2) \cdot x^{-2-1}$

4. Thanks guys!