Differentiate the function with respect to x : ( x ) - Vidyadip

Question

Differentiate the function with respect to x : $\sec \left( {\tan \sqrt x } \right)$

✓

Answer

Let $y = \sec \left( {\tan \sqrt x } \right)$

$\therefore \frac{{dy}}{{dx}} = \sec \left( {\tan \sqrt x } \right)\tan \left( {\tan \sqrt x } \right)\frac{d}{{dx}}\left( {\tan \sqrt x } \right)$

$= \sec \left( {\tan \sqrt x } \right)\tan \left( {\tan \sqrt x } \right){\sec ^2}\sqrt x \frac{d}{{dx}}\sqrt x $

$= \sec \left( {\tan \sqrt x } \right)\tan \left( {\tan \sqrt x } \right){\sec ^2}\sqrt {x.} \frac{1}{2}{x^{\frac{1}{2} - 1}}$

$= \sec \left( {\tan \sqrt x } \right)\tan \left( {\tan \sqrt x } \right){\sec ^2}\sqrt x .\frac{1}{{2\sqrt x }}$

$= \frac{{\sec \left( {\tan \sqrt x } \right).\tan \left( {\tan \sqrt x } \right).{{\sec }^2}\sqrt x }}{{2\sqrt x }}$

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 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

Evaluate:
$\cot\Big(\sin^{-1}\frac{3}{4}+\sec^{-1}\frac{4}{3}\Big)$

Find the angle at which the following vectors are inclined to each of the coordinate axes: $\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}}$

Write a value of $\int\tan\text{x}\sec^3\text{x dx}$

Compute the products AB and BA whichever exists the following cases:
$\text{A}=\begin{bmatrix}1&-2\\2&3\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}$

Write the coefficient a, b, c of which the value of the integral $\int\limits^3_{-3}(\text{ax}^2+\text{bx}+\text{c})\text{dx}$ is independent.

What is the range of the function $\text{f(x)}=\frac{|\text{x}-1|}{\text{x}-1}?$

Integrate the function: $\frac{{\cos \sqrt x }}{{\sqrt x }}$

Write the cartesian and vector equations of y-axis.

Evaluate the product $\big(3\vec{a}-5\vec{b})\cdot\big(2\vec{a}+7\vec{b}).$

Write the smallest reflexive relation on set $A=\{1,2,3,4\}$.