d dx ( x^3 ^2 x 2 )= - Vidyadip

MCQ

${d \over {dx}}\left( {{x^3}{{\tan }^2}{x \over 2}} \right)=$

A
${x^3}\tan {x \over 2}.{\sec ^2}{x \over 2} + 3x{\tan ^2}{x \over 2}$
✓
${x^3}\tan {x \over 2}.{\sec ^2}{x \over 2} + 3{x^2}{\tan ^2}{x \over 2}$
C
${x^3}{\tan ^2}{x \over 2}.{\sec ^2}{x \over 2} + 3{x^2}{\tan ^2}{x \over 2}$
D
એક પણ નહીં

✓

Answer

Correct option: B.

${x^3}\tan {x \over 2}.{\sec ^2}{x \over 2} + 3{x^2}{\tan ^2}{x \over 2}$

b
(b) $\frac{d}{{dx}}\left( {{x^3}{{\tan }^2}\frac{x}{2}} \right) = 3{x^2}{\tan ^2}\frac{x}{2} + 2{x^3}\tan \frac{x}{2}{\sec ^2}\frac{x}{2}.\frac{1}{2}$

$ = {x^3}\tan \frac{x}{2}{\sec ^2}\frac{x}{2} + 3{x^2}{\tan ^2}\frac{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

જો $f(y) = {e^y},\,g(y) = y;\,y > 0$ અને $F(t) = \int_{\,0}^{\,t} {\,f(t - y)\,g(y)\,dy,} $ તો . . .

${d \over {dx}}{\tan ^{ - 1}}\left[ {{{3{a^2}x - {x^3}} \over {a({a^2} - 3{x^2})}}} \right]$ એ $x = 0$ આગળ મેળવો.

$ \int \frac{e^x-1}{e^x+1} dx$ = ___________ + c

વિધેય $f(x) = {{4{x^2} + 1} \over x}$ એ. . . .અંતરાલમાં ઘટતું વિધેય છે .

જો સદિશો $\overrightarrow a $ અને $\overrightarrow b $ માટે $\left| {\overrightarrow a + \overrightarrow b } \right| = \sqrt {29} $ અને $\overrightarrow a \times \left( {2\hat i + 3\hat j + 4\hat k} \right) = \left( {2\hat i + 3\hat j + 4\hat k} \right) \times \overrightarrow b $ હોય,તો $\left( {\overrightarrow a + \overrightarrow b } \right).\left( { - 7\hat i + 2\hat j + 3\hat k} \right)$ નું શકય મૂલ્ય $.........$

જો $y = f(x) = \frac{{ax + b}}{{cx - a}}$, તો $x$ મેળવો

જો $f(x) = x^4+ \lambda x^3 +x^2$ $(\lambda \in R)$ ને $\frac{1}{2} $ આગળ સ્થાનીય મહત્તમ કિમત મળે તો $f(x)$ ચોક્કસ ન્યુન્તમ કિમત મેળવો.

$\int_{}^{} {\frac{{x - 2}}{{{x^2} - 4x + 3}}dx = } $

જો $\omega = - \frac{1}{2} + i\frac{{\sqrt 3 }}{2}$. તો $\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{ - 1 - {\omega ^2}}&{{\omega ^2}}\\1&{{\omega ^2}}&{{\omega ^4}}\end{array}\,} \right|= . . . $

$\int\limits_0^{\frac{1}{2}} {\frac{{\ln \left( {1 + 2x} \right)}}{{1 + 4{x^2}}}} \,dx$ =