Differentiate the following functions with respect to x: ( ) - Vidyadip

Question

Differentiate the following functions with respect to x:
$\sin(\log\sin\text{x})$

✓

Answer

Consider $\text{y}=\sin(\log\sin\text{x})$
Differentiate with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{\text{d}}{\text{dx}}\sin(\log\sin\text{x})$
$=\cos(\log\sin\text{x})\frac{\text{d}}{\text{dx}}(\log\sin\text{x})$
[Using chain rule]
$=\cos(\log\sin\text{x})\times\frac{1}{\sin\text{x}}\frac{\text{d}}{\text{dx}}0\sin\text{x}$
$=\cos(\log\sin\text{x})\frac{\cos\text{x}}{\sin\text{x}}$
$=\cos(\log\sin\text{x})\times\cot\text{x}$
Hence, the solution is, $\frac{\text{d}}{\text{dx}}(\sin(\log\sin\text{x}))=\cos(\log\sin\text{x})\text{x}\cot\text{x}$

Need a full question paper?

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

Start Generating Free

Explore more

More "3 Marks" from CONTINUITY AND DIFFERENTIABILITY→CONTINUITY AND DIFFERENTIABILITY — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the area of the parallelogram whose diagonals are:
$4\hat{\text{i}}-\hat{\text{j}}-3\hat{\text{k}}$ and $-2\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}$

A man wins a rupee for head and loses a rupee for tail when a coin is tossed. Suppose that he tosses once and quits if he wins but tries once more if he loses on the first toss. Find the probability distribution of the number of rupees the man wins.

Find $\frac{\text{dy}}{\text{dx}},\ \text{if y}=12(1-\cos \text{t}),\ \text{x}=10(\text{t}-\sin\text{t}),\ -\frac{\pi}{2}<\text{t}<\frac{\pi}{2}$

Represent the following families of curves by forming the corresponding differential equation:
$\text{y}=4\text{ax}$

Solve for x and y:
$\text{x}\begin{bmatrix}2\\1\end{bmatrix}+\text{y}\begin{bmatrix}3\\5\end{bmatrix}+\begin{bmatrix}-8\\-11\end{bmatrix}=0.$

If y = cos^-1x. Find $\frac{{{d^2}y}}{{d{x^2}}}$ in terms of y alone.

If $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=\vec{0,}$ show that the angle $\theta$ between the vectors $\vec{\text{b}}$ and $\vec{\text{c}}$ is given by

$\cos\theta=\frac{|\vec{\text{a}}|^2-\big|\vec{\text{b}}\big|^2-|\vec{\text{c}}|^2}{2\big|\vec{\text{b}}\big||\vec{\text{c}}|}.$

In a 20-question true-false examination, suppose a student tosses a fair coin to determine his answer to each question. For every head, he answers 'true' and for every tail, he answers 'false'. Find the probability that he answers at least 12 questions correctly.

Find adjoint of the matrix $\left|\begin{array}{ccc}1 & -1 & 2 \\ 2 & 3 & 5 \\ -2 & 0 & 1\end{array}\right|$

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors $\overrightarrow{\text{OP}}=2\vec{\text{a}}+\vec{\text{b}}\text{ and }\overrightarrow{\text{OQ}}=\vec{\text{a}}-2\vec{\text{b}}$, respectively in the ratio 1 : 2 internally and externally.