Question
Differentiate the following functions with respect to x:
$\sin(\log\text{x})$
$\sin(\log\text{x})$
✓
Answer
Consider $\text{y}=\sin(\log\text{x})$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\sin(\log\text{x})$
$=\cos(\log\text{x})\frac{\text{d}}{\text{dx}}(\log\text{x})$
[Using chain rule]
$=\frac{1}{\text{x}}\cos(\log\text{x})$
Hence, the solution is $\frac{\text{d}}{\text{dx}}=(\sin(\log\text{x}))=\frac{1}{\text{x}}\cos(\log\text{x})$
Differentiate it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\sin(\log\text{x})$
$=\cos(\log\text{x})\frac{\text{d}}{\text{dx}}(\log\text{x})$
[Using chain rule]
$=\frac{1}{\text{x}}\cos(\log\text{x})$
Hence, the solution is $\frac{\text{d}}{\text{dx}}=(\sin(\log\text{x}))=\frac{1}{\text{x}}\cos(\log\text{x})$
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