d dx ( e^ 1 - x^2 . x ) - Vidyadip

MCQ

$\frac{d}{{dx}}\left( {{e^{\sqrt {1 - {x^2}} }}.\tan x} \right)$

A
${e^{\sqrt {1 - {x^2}} }}\left[ {{{\sec }^2}x + \frac{{x\tan x}}{{\sqrt {1 - {x^2}} }}} \right]$
✓
${e^{\sqrt {1 - {x^2}} }}\left[ {{{\sec }^2}x - \frac{{x\tan x}}{{\sqrt {1 - {x^2}} }}} \right]$
C
${e^{\sqrt {1 - {x^2}} }}\left[ {{{\sec }^2}x + \frac{{\tan x}}{{\sqrt {1 - {x^2}} }}} \right]$
D
None of these

✓

Answer

Correct option: B.

${e^{\sqrt {1 - {x^2}} }}\left[ {{{\sec }^2}x - \frac{{x\tan x}}{{\sqrt {1 - {x^2}} }}} \right]$

b
(b) $\frac{d}{{dx}}\left[ {{e^{\sqrt {1 - {x^2}} }}\tan x} \right]$
$ = {e^{\sqrt {1 - {x^2}} }}\frac{1}{{2\sqrt {1 - {x^2}} }}( - 2x)\tan x + {e^{\sqrt {1 - {x^2}} }}{\sec ^2}x$
$ = {e^{\sqrt {1 - {x^2}} }}\left[ {{{\sec }^2}x - \frac{{x\tan x}}{{\sqrt {1 - {x^2}} }}} \right]$.

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 closed vessel tapers to a point both at its top $E$ and its bottom $F$ and is fixed with $EF$ vertical when the depth of the liquid in it is $x\,\, cm$, the volume of the liquid in it is, $ x^2 (15 - x) \,\,cu. cm.$ The length $EF$ is ........ $cm $.

Let $A =$ $\left[ {\begin{array}{*{20}{c}}{1 + {x^2} - {y^2} - {z^2}}&{2(xy + z)}&{2(zx - y)}\\{2(xy - z)}&{1 + {y^2} - {z^2} - {x^2}}&{2(yz + x)}\\{2(zx + y)}&{2(yz - x)}&{1 + {z^2} - {x^2} - {y^2}}\end{array}} \right]$ then det. $A$ is equal to

If $\int_{0}^{\pi}\left(\sin ^{3} x\right) e^{-\sin ^{2} x} d x=\alpha-\frac{\beta}{e} \int_{0}^{1} \sqrt{t} e^{t} d t$, then $\alpha+\beta$ is equal to $....$

$\left( {\int_{\,0}^{\,a} {x\,dx} } \right) \le (a + 4),$ then

If $A = \left( {\begin{array}{*{20}{c}}1&{ - 2}&1\\2&1&3\end{array}} \right)$ and $B = \left( {\begin{array}{*{20}{c}}2&1\\3&2\\1&1\end{array}} \right)$, then ${(AB)^T}$ is equal to

If $y = {{{a^{{{\cos }^{ - 1}}x}}} \over {1 + {a^{{{\cos }^{ - 1}}x}}}}$ and $z = {a^{{{\cos }^{ - 1}}x}}$, then ${{dy} \over {dz}}=$

A biased die is tossed and the respective probabilities for various faces to turn up are given below

$Face:$	$1$	$2$	$3$	$4$	$5$	$6$
$P(F)$	$0.1$	$0.24$	$0.19$	$0.18$	$0.15$	$0.14$

If an even face has turned up, then the probability that it is face $2$ or face $4$, is

Let $A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2\end{array}\right]$. If $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A))|=(16)^{ n }$, then $n$ is equal to

If $y = {\tan ^{ - 1}}{x \over {1 + \sqrt {1 - {x^2}} }} + \sin \left\{ {2{{\tan }^{ - 1}}\sqrt {\left( {{{1 - x} \over {1 + x}}} \right)} } \right\}$, then ${{dy} \over {dx}} =$

A random variable X has the following probability distribution:

X:	1	2	3	4	5	6	7	8
P(X):	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

Find the events E = {X : X is a prime number}, F{X : X < 4}, the probability $\text{P}(\text{E}\cup\text{F})$ is:

0.50
0.77
0.35
0.87