Derivative With Logs

**Chuglife** · October 23rd 2011, 07:12 PM

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

**Prove It** · October 23rd 2011, 07:15 PM

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

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

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

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