d dx [ ^ - 1 ( x) + ^ - 1 ( x)] = - Vidyadip

MCQ

${d \over {dx}}[{\tan ^{ - 1}}(\cot x) + {\cot ^{ - 1}}(\tan x)] = $

A
$0$
B
$1$
C
$-1$
✓
$-2$

✓

Answer

Correct option: D.

$-2$

d
(d) $\frac{d}{{dx}}[{\tan ^{ - 1}}(\cot x) + {\cot ^{ - 1}}(\tan x)]$

=$\frac{{1( - {\rm{cose}}{{\rm{c}}^2}x)}}{{1 + {{\cot }^2}x}} - \frac{{1({{\sec }^2}x)}}{{1 + {{\tan }^2}x}} = - 1 - 1 = - 2$.

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 5. continuity and differentiation→5. continuity and differentiation — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

A ladder $10 \,m $ long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of $3\,\,cm/sec$. The height of the upper end while it is descending at the rate of $4 \,\, cm/sec$ is

If $A$ is any square matrix of order $3 \times 3 such$ that $|A|=3$, then the value of $|\operatorname{adj} A|$ is

$\int_{}^{} {\frac{{{e^{\sqrt x }}\cos {e^{\sqrt x }}}}{{\sqrt x }}dx} = $

If $f$ is a real- valued differentiable function satisfying $|f(x) - f(y)| \le {(x - y)^2},x,y \in R$ and $f(0) = 0$, then $f(1)$ equal

The value of $\int_1^2 {\log x\,dx} $ is

Let $f: R \rightarrow R$ be defined by $f(x)=2 x+\cos x$, then $f$

The solution of $\cos (x + y)\,dy = \,\,dx$ is

If a relation R is defined on the set Z of integers as follows: (a, b) ∈ R ⇔ a² + b² = 25. Then, domain (R) is:

{3, 4, 5}
{0, 3, 4, 5}
$\{0,\pm3,\pm4,\pm5\}$
None of these.

The value of $\cot \left(\sum_{n=1}^{23} \cot ^{-1}\left(1+\sum_{k=1}^n 2 k\right)\right)$ is

Consider the relations $R_1$ and $R_2$ defined as $a R_1 b$ $\Leftrightarrow a^2+b^2=1$ for all $a, b, \in R$ and $(a, b) R_2(c, d)$ $\Leftrightarrow a+d=b+c$ for all $(a, b),(c, d) \in N \times N$. Then