Download App

Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability2 Marks
Question
Find $\frac{{dy}}{{dx}},$ $y = {\sin ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right),0 < x < 1$
✓

Answer

Given: $y = {\sin ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right),0 < x < 1$ 
Putting $x = \tan \theta $ 
$y = {\sin ^{ - 1}}\left( {\frac{{1 - {{\tan }^2}\theta }}{{1 + {{\tan }^2}\theta }}} \right)$
$= {\sin ^{ - 1}}\left( {\cos 2\theta } \right)$
$= {\sin ^{ - 1}}\sin \left( {\frac{\pi }{2} - 2\theta } \right) = \frac{\pi }{2} - 2\theta$
$= \frac{\pi }{2} - 2{\tan ^{ - 1}}x$ 
$\therefore \frac{{dy}}{{dx}} = 0 - 2.\frac{1}{{1 + {x^2}}} = \frac{{ - 2}}{{1 + {x^2}}}$

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the equation of line joining (1, 2) and (3, 6) using determinants.
→
Write a value of $\int\frac{(\tan^{-1}\text{x})^3}{1+\text{x}^2}\text{dx}$
→
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
→
If $\text{y}=\sin^{-1}\text{x}+\cos^{-1}\text{x},$ find $\frac{\text{dy}}{\text{dx}}.$
→
Let $R_0$ denote the set of all non$-$zero real numbers and let $A = R_0 \times R_0$. If $'*\ '$ is a binary operation on adefined by,
$(a, b) * (c, d) = (ac, bd)$ for all $(a, b), (c, d) \in A$
Find the identity element in $A$
→
Find the domain of$\sec^{-1}(3\text{x}-1)$
→
Evaluate the following:
$\cot\Big(\cot^{-1}\frac{3}{5}\Big)$
→
If $\begin{vmatrix}2\text{x}+5&3\\5\text{x}+2&9\end{vmatrix}=0,$ find x.
→
Construct a $3 \times 4$ matrix $A = [a_{ij}]$ whose element $a_{ij}$ are given by:
$\text{a}_\text{ij}=\frac{1}{2}|-3\text{i}+\text{j}|$
→
Evaluate the definite integral $\int\limits_0^{\frac{\pi }{4}} {\sin 2xdx}$
→