MCQ
The derivative of x2 cos x is:
- A2x sin x - x2 sin x
- B2x cos x - x2 sin x
- C2x sin x - x2 cos x
- Dcosx - x2 sin x cos x
Solution:
$\frac{ \text{d}}{\text{dx}(\text{x}2 \text{cos x})}$
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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The tangent of angle between the lines whose intercepts on the axes are a, -b and b, -a, respectively, is
$\frac{\text{a}^2-\text{b}^2}{\text{ab}}$
$\frac{\text{b}^2-\text{a}^2}{2}$
$\frac{\text{b}^2-\text{a}^2}{2\text{ab}}$