Gradient of a potential energy function

[Radarithm]

Homework Statement

Find the derivative of $$\frac{Q}{4\pi \epsilon_0 r}$$

Homework Equations

$$\frac{d}{dx} \frac{1}{x}=\ln x$$

The Attempt at a Solution

Assuming $Q$ and the rest of the variables under it are constant, $$\frac{Q}{4\pi \epsilon_0}\frac{1}{r}$$ then the derivative should be $\ln r$. I am taking the gradient of a potential energy function but since it is in one dimension ($r$ in this case isn't a 2-3 dimensional vector) it is the same as taking the derivative. Is my answer correct or did I make a mistake somewhere?

 

[Mentallic]

You have it the wrong way around.

$$\frac{d}{dx}\ln{x}=\frac{1}{x}$$

 

[Radarithm]

You have it the wrong way around.

$$\frac{d}{dx}\ln{x}=\frac{1}{x}$$

Yep, thanks for correcting me. The derivative is then $$\frac{-1}{r^2}$$ from the power rule, correct?

 

[Mentallic]

Correct.