Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives2 Marks
Question
Differentiate the following functions with respect to x:$\frac{\text{e}^\text{x}+\sin\text{x}}{1+\log\text{x}}$
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Answer
We have, $\frac{\text{d}}{\text{dx}}\Big(\frac{\text{e}^\text{x}+\sin\text{x}}{1+\log\text{x}}\Big)$
Using Quotient rule, we get
$=\frac{(1+\log\text{x})\frac{\text{d}}{\text{dx}}(\text{e}^\text{x}+\sin\text{x})-(\text{e}^\text{x}+\sin\text{x})\frac{\text{d}}{\text{dx}}(1+\log\text{x})}{(1+\log\text{x})^2}$
$=\frac{(1+\log\text{x})(\text{e}^\text{x}+\cos\text{x})-(\text{e}^\text{x}+\sin\text{x})\frac{1}{\text{x}}}{(1+\log\text{x})^2}$
$=\frac{\text{x}(1+\log\text{x})(\text{e}^\text{x}+\cos\text{x})-(\text{e}^\text{x}+\sin\text{x})}{\text{x}(1+\log\text{x})^2}$
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