Differentiate ^3 x ^3 x w.r.t x - Vidyadip

Question

Differentiate $\sin ^3 x \cos ^3 x\ \ w.r.t\ x$

✓

Answer

We have, $\frac{d}{d x}\left(\sin ^3 x \cos ^3 x\right)=\sin ^3 x \cdot \frac{d}{d x} \cos ^3 x+\cos ^3 x \cdot \frac{d}{d x}\left(\sin ^3 x\right) [$Using Product Rule of differentiation$]$
$=\sin ^3 x \cdot 3 \cos ^2 x(-\sin x)+\cos ^3 x \cdot 3 \sin ^2 x \cdot \cos x$
$=-3 \sin ^4 x \cos ^2 x+3 \cos ^4 x \sin ^2 x$
$=3 \sin ^2 x \cos ^2 x\left(-\sin ^2 x+\cos ^2 x\right)$
$=3 \sin ^2 x \cos ^2 x \cdot \cos 2 x$
$=\frac{3}{4} \cdot 4 \sin ^2 x \cos ^2 x \cdot \cos 2 x$
$=\frac{3}{4}(2 \sin x \cos x)^2 \cos 2 x$
$=\frac{3}{4} \sin ^2 2 x \cdot \cos 2 x$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Model Paper 6→Model Paper 6 — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the coefficient of:
x in the expansion of $(1-2\text{x}^3+3\text{x}^5)\Big(1+\frac{1}{\text{x}}\Big)^8.$

Write $E = (14, 21, 28, 35, 42, ..., 98)$ in set$-$builder form.

A committee of 6 members is to be formed out of 8 men and 5 women. In how many ways can this committee be formed while in each committee :
(i) there should be only 2 men,
(ii) there should be only 2 women,
(iii) there should be at least two women,
(iv) there should be at least two men.

In how many ways can six persons be seated in a row?

Differentiate the following functions with respect to x:$\frac{\text{2x}-1}{\text{x}^2+1}$

If $A =\{x: x=2 n, n$ is a positive integer $\}$ and B $=\{x: x=3 n, n$ is a positive integer $\}$, then find the value of $A \cap B$.

How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?

Find the sum of the following geometric series:
$\text{x}^3,\text{x}^5,\text{x}^7,\ ...\ \text{to n terms}$

Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of a square.

The numbers $1, 2, 3$ and $4$ are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement.
Describe the following events:
$A =$ The number on the first slip is larger than the one on the second slip.
$B =$ The number on the second slip is greater than $2.$
$C =$ The sum of the numbers on the two slips is $6$ or $7$.
$D =$ The number on the second slips is twice that on the first slip.
Which pair$(s)$ of events is $($are$)$ mutually exclusive?