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Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives5 Marks
Question
Differentiate the following functions with respect to x:$\frac{\text{x}+\cos\text{x}}{\tan\text{x}}$
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Answer

We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}+\cos\text{x}}{\tan\text{x}}\Big)$
Using quotient rule, we get
$\frac{(\tan\text{x})\frac{\text{d}}{\text{dx}}(\text{x}+\cos\text{x})-(\text{x}+\cos\text{x})\frac{\text{d}}{\text{dx}}(\tan\text{x})}{(\tan^2\text{x})}$
$=\frac{\tan\text{x}\Big\{1+(-\sin\text{x})\Big\}-(\text{x}+\cos\text{x})\sec^2\text{x}}{(\tan^2\text{x})}$
$=\frac{(1-\sin\text{x})\tan\text{x}-(\text{x}+\cos\text{x})\sec^2\text{x}}{(\tan^2\text{x})}$

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