Question
Differentiate the following functions.
$\text{x}^{2}\sin\text{x}+\cos2\text{x}$
$\text{x}^{2}\sin\text{x}+\cos2\text{x}$
✓
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 $\text{x}^{2}\cos\text{x}+2\text{x}+2\text{x}\sin\text{x}-2\sin2\text{x}.$
$=\frac{\text{d}}{\text{dx}}(\text{x}^{2}\sin\text{x})+\frac{\text{d}}{\text{dx}}(\cos2\text{x})$
$=(\text{x}^{2}\cos\text{x}+\sin\text{x}.2\text{x})+(-2\sin2\text{x})$
$=\text{x}^{2}\cos\text{x}+2\text{x}+2\text{x}\sin\text{x}-2\sin2\text{x}$
Hence, the required answer is $\text{x}^{2}\cos\text{x}+2\text{x}+2\text{x}\sin\text{x}-2\sin2\text{x}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Consider the following population and year graph, find the slope of the line AB and using it, find what will be the population in the year 2010?
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{bx}-\text{e}^\text{ax}}{\text{x}}$ where 0 < a < b.
→$\lim\limits_{\text{x}\rightarrow0}\frac{\text{e}^\text{bx}-\text{e}^\text{ax}}{\text{x}}$ where 0 < a < b.
Prove that:
$\cos\frac{\pi}{12}-\sin\frac{\pi}{12}=\frac{1}{\sqrt2}$
→$\cos\frac{\pi}{12}-\sin\frac{\pi}{12}=\frac{1}{\sqrt2}$
Find the equation of two straight lines which are parallel to x + 7y + 2 = 0 and at unit distance from the point (1, -1).
Prove that $\lim _{x \rightarrow 0} \frac{\sqrt{1-x}-\sqrt{1+x}}{x}=-1.$
→$\frac{\cos2\text{A}}{\text{a}^2}-\frac{\cos2\text{B}}{\text{b}^2}=\frac{1}{\text{a}^2}-\frac{1}{\text{b}^2}$
→If three points (h, 0), (a, b) and (0, k) lies on a line, show that $\frac{a}{h} + \frac{b}{k} = 1$
→A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
Solve the inequality $\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}$ for real x.
→