Download App

STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
${d \over {dx}}{\cos ^{ - 1}}{{x - {x^{ - 1}}} \over {x + {x^{ - 1}}}} =$  
  • A
    ${1 \over {1 + {x^2}}}$
  • B
    ${{ - 1} \over {1 + {x^2}}}$
  • C
    ${2 \over {1 + {x^2}}}$
  • ✓
    ${{ - 2} \over {1 + {x^2}}}$
✓

Answer

Correct option: D.
${{ - 2} \over {1 + {x^2}}}$
d
(d) Putting $x = \cot \theta $

$y = {\cos ^{ - 1}}\left( {\frac{{x - {x^{ - 1}}}}{{x + {x^{ - 1}}}}} \right) = {\cos ^{ - 1}}\left( {\frac{{{x^2} - 1}}{{{x^2} + 1}}} \right)$

$ = {\cos ^{ - 1}}(\cos 2\theta ) = 2\theta $

$\Rightarrow \frac{{dy}}{{dx}} = \frac{{ - 2}}{{1 + {x^2}}}$.

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 "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

Let $f: R \rightarrow R$ be defined as

$f(x)=\left\{\begin{array}{ccc}x^{5} \sin \left(\frac{1}{x}\right)+5 x^{2}& , & x<0 \\ 0 & , & x=0 \\ x^{5} \cos \left(\frac{1}{x}\right)+\lambda x^{2} & , & x>0\end{array} .\right.$

The value of $\lambda$ for which $f^{\prime \prime}(0)$ exists, is

→
If $\frac{\pi }{2} \le x \le \frac{{3\pi }}{2},$ then ${\sin ^{ - 1}}(\sin x)$ is equal to
→
The primitive of the function $\text{f(x)}=\Big(1-\frac{1}{\text{x}^2}\Big)\text{a}^{\text{x}+\frac{1}{\text{x}}},\text{ a} > 0$ is :
→
Choose the correct answer from the given four options:
The area of the region bounded by the curve $\text{y}=\sin\text{x}$ between the ordinates x = 0, $\text{x}=\frac{\pi}{2}$ and the x-axis is:
→
Choose the correct answer from the given four options:The maximum value of $\sin\text{x}\cdot\cos\text{x}$ is:
→
Choose the correct answer from the given four options.The probability that a person is not a swimmer is $0.3.$ The probability that out of $5$ persons $4$ are swimmers is:
→
The differential equation which respresents the famliy of curves $\text{y}=\text{e}^{\text{Cx}}$ is :
→
$\int\frac{1}{1-\cos\text{x}-\sin\text{x}}\text{ dx}=$
→
If the function $\text{f}(\text{x})=\cos|\text{x}|-2\text{ax}+\text{b}$ increases along entire number scale, then:
→
$\int_{}^{} {x\sqrt {1 + {x^2}} } \;dx = $
→