Differentiate the following functions. x^ 2 + 2x - Vidyadip

Question

Differentiate the following functions.
$\text{x}^{2}\sin\text{x}+\cos2\text{x}$

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Answer

$\frac{\text{d}}{\text{dx}}(\text{x}^{2}\sin\text{x}+\cos2\text{x})$
$=\frac{\text{d}}{\text{dx}}(\text{x}^{2}\sin\text{x})+\frac{\text{d}}{\text{dx}}(\cos2\text{x})$
$=(\text{x}^{2}\cos\text{x}+\sin\text{x}.2\text{x})+(-2\sin2\text{x})$
$=\text{x}^{2}\cos\text{x}+2\text{x}+2\text{x}\sin\text{x}-2\sin2\text{x}$
Hence, the required answer is $\text{x}^{2}\cos\text{x}+2\text{x}+2\text{x}\sin\text{x}-2\sin2\text{x}.$

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