Download App

5. continuity and differentiation — ગણિત ધોરણ 12 સાયન્સ — Question

Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિત5. continuity and differentiation1 Mark
MCQ
${d \over {dx}}{\left( {\sqrt x + {1 \over {\sqrt x }}} \right)^2} = $
  • ✓
    $1 - {1 \over {{x^2}}}$
  • B
    $1 + {1 \over {{x^2}}}$
  • C
    $1 - {1 \over {2x}}$
  • D
    એકપણ નહીં
✓

Answer

Correct option: A.
$1 - {1 \over {{x^2}}}$
a
(a) $\frac{d}{{dx}}{\left( {\sqrt x + \frac{1}{{\sqrt x }}} \right)^2} = \frac{d}{{dx}}\left[ {x + \frac{1}{x} + 1} \right] = 1 - \frac{1}{{{x^2}}}$.

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 "MCQ" from 5. continuity and differentiation→5. continuity and differentiation — all question types→ગણિત ધોરણ 12 સાયન્સ question papers→Gujarat Board ધોરણ 12 સાયન્સ question papers→Gujarat Board question paper generator→

Similar questions

$f(x) = 1 + 2 sinx + 3cos^2x (0 < x < 2\pi /3) $ તો......
→
$\int_{}^{} {\frac{{dx}}{{x\log x\log (\log x)}} = } $
→
$\begin{vmatrix}1^2 & 5^2 & 3^2 \\ 2^2 & 25^2 & 24^2 \\ 3^2 & 41^2 & 40^2\end{vmatrix} +\begin{vmatrix}1^2 & 5^2 & 4^2 \\ 2^2 & 25^2 & 7^2 \\ 3^2 & 41^2 & 9^2\end{vmatrix} =\ldots \ldots \ldots$
→
જો $f(x) = \left\{ \begin{array}{l}x,\,\,{\rm{when\,\,}}\,x\,\,{\rm{\,is\,}}\,{\rm{\,rational\,\,}}\\0{\rm{,}}\,\,{\rm{when\,\,}}x{\rm{ \,\,is\,\,\, irrational\,}}\end{array} \right.$;

$g(x) = \left\{ \begin{array}{l}0,\,\,\,\,{\rm{when\,\,}}\,x\,{\rm{\,\,is\,\,}}\,{\rm{\,\,rational\,}}\\x,\,\,\,\,{\rm{\,\,when\,\,}}\,x\,{\rm{\,\,is\,\, irrational\,}}\end{array} \right.$ તો $(f - g)  =$

→
જો સદીશો $\hat i + \lambda \hat j + \hat k$, $\hat j + \lambda \hat k$ અને $\lambda \hat i + \hat k$ થી બનતા સમાંતર ફલકનું ઘનફળ ન્યૂનતમ હોય તો  $\lambda $ મેળવો.
→
જો $y = 2x + {\cot ^{ - 1}}\,x + \log \left( {\sqrt {1 + {x^2}}  - x} \right),$ હોય તો $y$ એ
→
વિકલ સમીકરણ $\frac{{dy}}{{dx}} + y{\sec ^2}x = \tan x{\sec ^2}x$ નો ઉકેલ મેળવો.
→
$\left[ {x\,y\,z} \right]\,\left[ {\begin{array}{*{20}{c}}
a&h&g\\
h&b&f\\
g&f&c
\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}
x\\
y\\
z
\end{array}} \right]$ ની કક્ષા મેળવો.
→
જો $f(x) = \log x$ હોય તો $f[\log (x)]$ નું વિકલન મેળવો.
→
જો $y^{2}+\log _{e}\left(\cos ^{2} x\right)=y, x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right),$ હોય તો 
→