Question
Differentiate the following function with respect to x:
$\log_{\text{x}^2}\text{x}$
✓
Answer
$\log_{\text{x}^2}\text{x}=\frac{\log\text{x}}{\log\text{x}^2}$ (By change of base property)
$=\frac{\log\text{x}}{2\log\text{x}}[\log\text{x}^2=2\log\text{x}]$
$=\frac{1}{2}$
Now
$\frac{\text{d}}{\text{dx}}(\log_{\text{x}^2}\text{x})=\frac{\text{d}}{\text{dx}}\Big(\frac{1}{2}\Big)$$=0(\because\frac{1}{2}$ is a constant)
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