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
The differential coefficient of the given function ${\log _e}\left( {\sqrt {{{1 + \sin x} \over {1 - \sin x}}} } \right)$ with respect to  $x $ is
  • A
    $cosec\,x$
  • B
    $\tan x$
  • C
    $\cos x$
  • ✓
    $\sec x$
✓

Answer

Correct option: D.
$\sec x$
d
(d) $\frac{{dy}}{{dx}} = \frac{1}{{\left( {\frac{{1 + \sin x}}{{\cos x}}} \right)}}\left[ {\frac{{\cos x\cos x + (1 + \sin x)\sin x}}{{{{(\cos x)}^2}}}} \right]$

$ = \left( {\frac{{\cos x}}{{1 + \sin x}}} \right)\frac{{{{\cos }^2}x + {{\sin }^2}x + \sin x}}{{{{(\cos x)}^2}}} = \sec 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 "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 $\overrightarrow {AO} + \overrightarrow {OB} = \overrightarrow {BO} + \overrightarrow {OC} ,$ then $A, B, C$ form
→
If the volume of a spherical ball is increasing at the rate of $4 \pi \, cc/sec$, then the rate of increase of its radius (in $cm/sec$), when the volume is $288 \pi \, cc$
→
If abscissa of vertex of parabola $y = a{x^2} + bx + c$ is $1\left( {a,b,c > 0} \right)$ and $f(x) = \int\limits_0^x {\left( {3a{x^2} + bx + c} \right)dx} $ is strictly increasing function $\forall \,\,\,x\, \in \,R$ , then maximum possible value of $\left[ {\frac{a}{c}} \right]$ is (where [.] denotes greatest integer function)
→
If $A=\left(\begin{array}{cc}0 & \sin \alpha \\ \sin \alpha & 0\end{array}\right)$ and $\operatorname{det}\left(A^{2}-\frac{1}{2} I\right)=0,$ then a possible value of $\alpha$ is
→
The equation of the plane passing through $(2, −3, 1)$ and is normal to the line joining the points $(3, 4, −1)$ and $(2, −1, 5)$ is given by:
→
Let $l =\mathop {Lim}\limits_{x \to \infty } \,\,\int\limits_x^{2x} {\frac{{dt}}{t}} $ and $m = \frac{1}{{x\,\ln \,x}}\,\,\int\limits_1^x {\ln \,t\,dt} $ then the correct statement is
→
Find the equation of the plane passing through the points $P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4):$
→
Let $f : R \rightarrow R$ be defind by $\text{f(x)}=\frac{1}{\text{x}}\forall\times\in\text{ R}.$ Then $f$ is:
→
$\int \frac{d x}{x \log _e x}$ is equal to :
→
If the function  $f(x) =  - 4{e^{\left( {\frac{{1 - x}}{2}} \right)}} + 1 + x + \frac{{{x^2}}}{2} + \frac{{{x^3}}}{3}$ and $g(x)=f^{-1}(x) \,;$ then the value of $g'(-\frac{7}{6})$ equals
→