Differentiate the following function with respect to (x): _3x+3 _… - Vidyadip

Question

Differentiate the following function with respect to $(\text{x})$:$\log_3\text{x}+3\log_\text{e}\text{x}+2\tan\text{x}$

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Answer

We have,$\frac{\text{d}}{\text{dx}}(\log_3\text{x}+3\log_\text{e}\text{x}+2\tan\text{x})$
$=\frac{1}{\log3}\frac{\text{d}}{\text{dx}}(\log\text{x})+3\frac{\text{d}}{\text{dx}}(\log_\text{e}\text{x})+2\frac{\text{d}}{\text{dx}}(\tan\text{x})\ \Bigg[\because\log_3\text{x}=\frac{\log\text{x}}{\log3}\Bigg]$
$=\frac{1}{\log3}\times\frac{1}{\text{x}}+\frac{3}{\text{x}}+2\sec^2\text{x}$
$=\frac{1}{\text{x}\log3}+\frac{3}{\text{x}}+2\sec^2\text{x}$

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