Download App

5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $y = {x^{({x^x})}}$, then ${{dy} \over {dx}} = $
  • A
    $y[{x^x}(\log ex).\log x + {x^x}]$
  • B
    $y[{x^x}(\log ex).\log x + x]$
  • ✓
    $y[{x^x}(\log ex).\log x + {x^{x - 1}}]$
  • D
    $y[{x^x}({\log _e}x).\log x + {x^{x - 1}}]$
✓

Answer

Correct option: C.
$y[{x^x}(\log ex).\log x + {x^{x - 1}}]$
c
(c) $y = {x^{({x^x})}} \Rightarrow \log y = {x^x}\log x$

==> $\frac{1}{y}\frac{{dy}}{{dx}} = \frac{{dz}}{{dx}}.\log x + \frac{1}{x}.z$ , (where ${x^x} = z$)

$ \Rightarrow \frac{{dy}}{{dx}} = {x^{({x^x})}}\left[ {{x^x}(\log ex).\log x + {x^{x - 1}}} \right]$,      $\left\{ \because \frac{dz}{dx}={{x}^{x}}\log ex \right\}$.

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

If $\frac{d y}{d x}=\frac{x+y}{x}, y(1)=1$, then $y=$
→
Let $\alpha $, $\beta$ $\gamma$, $\delta$ are distinct imaginary roots of

$z^5=1$ then value of $\left| {\begin{array}{*{20}{c}}
  {{e^\alpha }}&{{e^{2\alpha }}}&{{e^{3\alpha  + 1}}}&{ - {e^{ - \delta }}} \\ 
  {{e^\beta }}&{{e^{2\beta }}}&{{e^{3\beta  + 1}}}&{ - {e^{ - \delta }}} \\ 
  {{e^\gamma }}&{{e^{2\gamma }}}&{{e^{3\gamma  + 1}}}&{ - {e^{ - \delta }}} 
\end{array}} \right|$

→
Choose the correct answer from the given four options.
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is:
  1. Reflexive.
  2. Transitive.
  3. Symmetric.
  4. None of these.
→
If ${x^2} + {y^2} = t - {1 \over t},$ ${x^4} + {y^4} = {t^2} + {1 \over {{t^2}}}$, then ${x^3}y{{dy} \over {dx}} = $
→
Functions $f(x)$ and $g(x)$ are such that $f(x) + \int\limits_0^x {g(t)dt = 2\,\sin \,x\, - \,\frac{\pi }{2}} $ and $f'(x).g (x) = cos^2\,x$ , then number of solution $(s)$ of equation $f(x) + g(x) = 0$ in $(0,3 \pi$) is-
→
If the function $f(x)\, = \left\{ {\begin{array}{*{20}{c}}{ - x,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x < 1\,\,\,\,}\\{a + {{\cos }^{ - 1}}(x + b),\,\,\,\,\,\,\,\,\,1 \le x \le 2} \end{array}} \right.$  is differentiable at $x = 1 ,$ then $\frac {a}{b}$ is equal to 
→
$\sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2}$, then $x=$ _________.
→
$Let\,\,f(x) = \left\{ {\begin{array}{*{20}{c}}
  {{x^2} - a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;\,\,x < 3} \\ 
  {b\sqrt {x - 2}  + a\,\,\,\,\,\,\,\,\,\,\,;\,\,3 \leqslant x < 6.} \\ 
  {2x + b\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;\,\,\,x \geqslant 6} 
\end{array}} \right.$ If $f(x)$ is continuous $\forall x \in R$, then value of $\frac{f(1)-f(3)}{4}$

 

→
The length of the $\perp$
→
Choose the correct answer from the given four options.
Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections from A into B is:
  1. nP2
  2. 2n – 2
  3. 2n – 1
  4. None of these.
→