The derivative of x^2 x is: - Vidyadip

MCQ

The derivative of $x^2 \cos x$ is:

A
$2x \sin x - x^2 \sin x$
✓
$2x \cos x - x^2 \sin x$
C
$2x \sin x - x^2 \cos x$
D
$\cos x - x^2 \sin x \cos x$

✓

Answer

Correct option: B.

$2x \cos x - x^2 \sin x$

$\frac{ \text{d}}{\text{dx}(x^2 \text{cos x})}$
Using the formula $ \frac{\text{d}}{\text{dx} [\text{f(x) g(x)}]} = \text{f}(\text{x}) \Big[\frac{\text{d}}{\text{dx} \text{g}(\text{x})}\Big] + \text{g(x)} \Big[\frac{\text{d}}{\text{dx} \text{f(x})}\Big]$
$= \frac{\text{d}}{\text{dx}(\text{x}^2 \cos \text{x})}$
$= \text{x}^2 \Big[\frac{\text{d}}{\text{dx} (\cos \text{x})}\Big] + \cos x \Big[\frac{\text{d}}{\text{dx } \text{x}^2}\Big]$
$ = \text{x}^2(-\sin \text{x}) + \cos\text{x}(2\text{x})$
$ = 2\text{x} \cos \text{x} – \text{x}2 \sin \text{x}$

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