Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives2 Marks
Question
Differentiate the following function with respect to $\text{x}:$$\text{x}^\text{n}\tan\text{x}$
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Answer
Let $\text{u}=\text{x}^\text{n};\text{v}=\tan\text{x}$Then, $\text{u}'=\text{nx}^{\text{n}-1};\text{v}'=\sec^2\text{x}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uv})=\text{uv}'+\text{vu}'$
$\frac{\text{d}}{\text{dx}}(\text{x}^\text{n}\tan\text{x})=\text{x}^\text{n}\sec^2\text{x}+\tan\text{x}(\text{nx}^{\text{n}-1})$
$=\text{x}^{\text{n}-1}(\text{x}\sec^2\text{x}+\text{n}\tan\text{x})$
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