d dx ( e^x 1 + x^2 ) = - Vidyadip

MCQ

${d \over {dx}}\left( {{{{e^x}} \over {1 + {x^2}}}} \right) = $

A
${{{e^x}(1 + x)} \over {{{(1 + {x^2})}^2}}}$
✓
${{{e^x}{{(1 - x)}^2}} \over {{{(1 + {x^2})}^2}}}$
C
${{{e^x}{{(1 + x)}^2}} \over {(1 + {x^2})}}$
D
${{{e^x}{{(1 - x)}^2}} \over {(1 + {x^2})}}$

✓

Answer

Correct option: B.

${{{e^x}{{(1 - x)}^2}} \over {{{(1 + {x^2})}^2}}}$

b
(b) $\frac{d}{{dx}}\left( {\frac{{{e^x}}}{{1 + {x^2}}}} \right) = \frac{{(1 + {x^2}){e^x} - {e^x}(2x)}}{{{{(1 + {x^2})}^2}}} = \frac{{{e^x}{{(1 - x)}^2}}}{{{{(1 + {x^2})}^2}}}$

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

Let the relations $R_1$ and $R_2$ on the set $\mathrm{X}=\{1,2,3, \ldots, 20\}$ be given by $\mathrm{R}_1=\{(\mathrm{x}, \mathrm{y}): 2 \mathrm{x}-3 \mathrm{y}=2\}$ and $\mathrm{R}_2=\{(\mathrm{x}, \mathrm{y}):-5 \mathrm{x}+4 \mathrm{y}=0\}$. If $\mathrm{M}$ and $\mathrm{N}$ be the minimum number of elements required to be added in $R_1$ and $R_2$, respectively, in order to make the relations symmetric, then $\mathrm{M}+\mathrm{N}$ equals

$\left| {\,\begin{array}{*{20}{c}}1&1&1\\a&b&c\\{{a^3}}&{{b^3}}&{{c^3}}\end{array}\,} \right| = $

The number of bijective functions from set $A$ to itself when $A$ contains 106 elements is

If the binary operation $\odot$ is defined on the set Q⁺ of all positive rational numbers by $\text{a}\odot\text{b}=\frac{\text{ab}}4$. Then, $3\odot\Big(\frac{1}5\odot\frac{1}2\Big)$ is equal to:

$\frac{3}{160}$
$\frac{5}{160}$
$\frac{3}{10}$
$\frac{3}{40}$

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

9, 7, 4, 0
0, 2, 4, 6
6, 7, 7, 2
6, 4,2, 0

The value of a for which the function $\text{f(x)}=\begin{cases}5\text{x}-4,&\text{if }0<\text{x}\leq1\\4\text{x}^2+3\text{ax},&\text{if }<\text{x}<2\end{cases}$ is continuous at every point of its domain, is:

$\frac{13}{3}$
1
0
-1

If A is a matrix of order m × n and B is a matrix such that AB^Tand B^TA are both defined, then the order of matrix B is:

m × m
n × n
n × m
m × n

The minimum value of Z = 3x + 5y subjected to constraints $\text{x}+3\text{y}\geq3,\text{x}+\text{y}\geq2,\text{x},\text{y}\geq0$ is:

The solution of the differential equartion $\frac{\text{dy}}{\text{dx}}-\frac{\text{y}(\text{x}+1)}{\text{x}}=0$ is given by:

$\text{y}=\text{xe}^{\text{x}+\text{C}}$
$\text{x}=\text{ye}^{\text{x}}$
$\text{y}=\text{x}+\text{c}$
$\text{xy}=\text{e}^{\text{x}}+\text{C}$

$\text{A}^2=\text{I}\Rightarrow$

$|\text{A}|=0$
$|\text{A}|=1$
$|\text{A}|=-1$
$|\text{A}|=\pm1$