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Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives2 Marks
Question
Differentiate the following function with respect to $(\text{x})$:$\frac{1}{\sin\text{x}}+2^{\text{x}+3}+\frac{4}{\log\text{x}^3}$
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Answer

We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{1}{\sin\text{x}}+2^{\text{x}+3}+\frac{4}{\log\text{x}^3}\Big)$
$=\frac{\text{d}}{\text{dx}}\text{cosec}\text{x}+2^2\frac{\text{d}}{\text{dx}}(2^{\text{x}})+\frac{4}{\log3}\times\frac{\text{d}}{\text{dx}}(\log\text{x})\ \Big[\because\log_\text{b}\text{a}=\frac{\log\text{a}}{\log\text{b}}\Big]$
$=-\text{coesc}\text{x}.\cot\text{x}+8.2^\text{x}\log2+\frac{4}{\log3}\times\frac{1}{\text{x}}\ \Big[\because\frac{\text{d}}{\text{dx}}(\text{a}^\text{x})=\text{a}^\text{x}\log\text{a}\Big]$
$=-\text{coesc}\text{x}.\cot\text{x}+2^{\text{x}+3}\log2+\frac{4}{\text{x}\log3}$

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