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}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
If $2\tan\alpha=3\tan\beta$ then $\tan(\alpha-\beta)=$
$\sin\text{x}+\text{i}\cos2\text{x}$ and $\cos\text{x}-\text{i}\sin2\text{x}$ are conjugate to each other for:
$\text{x}=\text{n}\pi$
$\text{x}=\Big(\text{n}+\frac{1}{2}\Big)\frac{\pi}{2}$
$\text{x}=0$
no value of x
If X = {8n - 7n - 1 | n $\in$ N} and Y = {49n - 49 | n $\in$ N}. Then
$\text{X} \subset \text{Y}$
$\text{Y} \subset \text{X}$
$\text{X} = \text{Y}$
$\text{X} \cap \text{Y} = \phi$