CBSE BoardEnglish MediumSTD 11 ScienceMathsDerivatives3 Marks
Question
Differentiate the following functions with respect to x:$\frac{\text{x}^\text{n}}{\sin\text{x}}$
✓
Answer
We have,$\frac{\text{d}}{\text{dx}}\Big(\frac{\text{x}^\text{n}}{\sin\text{x}}\Big)$
$=\text{x}^\text{n}\frac{\text{d}}{\text{dx}}(\sin\text{x})^{-1}+\frac{1}{\sin\text{x}}\frac{\text{d}}{\text{dx}}(\text{x}^\text{n})$
$=\text{x}^\text{n}\frac{-1}{\sin^2\text{x}}+\frac{1}{\sin\text{x}}\text{n}\text{x}^{\text{n}-1}$
$=\frac{\sin\text{x}(\text{nx}^{\text{n}-1})-\text{x}^\text{n}(\cos\text{x})}{\sin^2\text{x}}$
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