Gujarat BoardEnglish MediumSTD 11 ScienceMATHSDerivatives2 Marks
Question
Differentiate the following function with respect to x:$\text{x}^2\sin\text{x}\log\text{x}$
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Answer
Let $\text{u}=\text{x}^\text{2};\text{v}=\sin\text{x};\text{w}=\log\text{x}$Then, $\text{u}'=2\text{x};\text{v}'=\cos\text{x};\text{w}'=\frac{1}{\text{x}}$
Using the product rule:
$\frac{\text{d}}{\text{dx}}(\text{uvw})=\text{u}'\text{vw}+\text{uw}\text{v}'+\text{uv}\text{w}'$
$\frac{\text{d}}{\text{dx}}(\text{x}^2\sin\text{x}\log\text{x})=2\text{x}\sin\text{x}\log\text{x}+\text{x}^2\cos\text{x}\log\text{x}+\text{x}^2\sin\text{x}.\frac{1}{\text{x}}$
$=2\text{x}\sin\text{x}\log\text{x}+\text{x}^2\cos\text{x}\log\text{x}+\text{x}\sin\text{x}$
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