Thread: Derivative With Logs

Hey I'm having trouble finding the derivative of problems that involve natural logs,

This is the problem i'm currently stuck on: y= (1+ ln x)/x^2

Originally Posted by Chuglife

Hey I'm having trouble finding the derivative of problems that involve natural logs,

This is the problem i'm currently stuck on: y= (1+ ln x)/x^2

You should know that $\displaystyle \displaystyle \frac{d}{dx}\left(\ln{x}\right) = \frac{1}{x}$.

In this case, you would need to use the quotient rule.

$\displaystyle \displaystyle \frac{d}{dx}\left(\frac{1+\ln{x}}{x^2}\right) = \frac{x^2\,\frac{d}{dx}\left(1 + \ln{x}\right) - \left(1 + \ln{x}\right)\frac{d}{dx}\left(x^2\right)}{\left(x ^2\right)^2}$