If y = ( ^ - 1 x), then dy dx is - Vidyadip

MCQ

If $y = \sec ({\tan ^{ - 1}}x),$ then ${{dy} \over {dx}}$ is

✓
${x \over {\sqrt {1 + {x^2}} }}$
B
${{ - x} \over {\sqrt {1 + {x^2}} }}$
C
${x \over {\sqrt {1 - {x^2}} }}$
D
None of these

✓

Answer

Correct option: A.

${x \over {\sqrt {1 + {x^2}} }}$

a
(a) $y = \sec ({\tan ^{ - 1}}x) {{dy} \over {dx}}$

$= \sec ({\tan ^{ - 1}}x) \tan ({\tan ^{ - 1}}x) \cdot \frac{{1}}{{1 + {x^2}}}$

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

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 "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If for $x \geq 0, y=y(x)$ is the solution of the differential equation $(\mathrm{x}+1) \mathrm{d} \mathrm{y}=\left((\mathrm{x}+1)^{2}+\mathrm{y}-3\right) \mathrm{d} \mathrm{x}, \mathrm{y}(2)=0$ then $y(3)$ is equal to

$\int\sec^2\text{x}.\operatorname{cosec}^2\text{xdx}=$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ and $\vec{\text{d}}$ are the position vector of points A, B, C, D such that no three of them are collinear and $\vec{\text{a}}+\vec{\text{c}}=\vec{\text{b}}+\vec{\text{d}}$, then ABCD is a,

For $a>0,$ let the curves $C_{1}: y^{2}=a x$ and $\mathrm{C}_{2}: \mathrm{x}^{2}=$ ay intersect at origin $\mathrm{O}$ and a point $\mathrm{P}$ Let the line $\mathrm{x}=\mathrm{b}(0<\mathrm{b}<\mathrm{a})$ intersect the chord $OP$ and the $\mathrm{x}$ -axis at points $\mathrm{Q}$ and $\mathrm{R}$, respectively. If the line $x=b$ bisects the area bounded by the curves, $\mathrm{C}_{1}$ and $\mathrm{C}_{2},$ and the area of $\Delta \mathrm{OQR}=\frac{1}{2},$ then '$a$' satisfies the equation

If $y=\cos ^2\left(\frac{3 x}{2}\right)-\sin ^2\left(\frac{3 x}{2}\right)$, then $\frac{d^2 y}{d x^2}$ is equal to

If $\mathrm{p}(\mathrm{x})$ be a polynomial of degree three that has a local maximum value $8$ at $x=1$ and a local minimum value $4$ at $x=2 ;$ then $p(0)$ is equal to

In a sphere the rate of change of surface area is:

In linear programming, oil companies used to implement resources available is classified as:

Evaluate: $\cos \left(\frac{\pi}{3}-\cos ^{-1} \frac{1}{2}\right)$

The points of discontinuity of the function $\text{f(x)}=\begin{cases}\frac{1}{5}(2\text{x}^2+3),&\text{x}\leq1\\6-5\text{x},&1<\text{x}<3\\\text{x}-3,&\text{x}\geq3\end{cases}$ is (are):