Download App

STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The solution of $\frac{{dy}}{{dx}} + \sqrt {\,\left( {\frac{{1 - {y^2}}}{{1 - {x^2}}}} \right)} \, = \,0$ is
→
Let,$S=\left\{\theta \in[0,2 \pi]: 8^{2 \sin ^{2} \theta}+8^{2 \cos ^{2} \theta}=16\right\}$. Then $n ( S )+\sum_{\theta \in S}\left(\sec \left(\frac{\pi}{4}+2 \theta\right) \operatorname{cosec}\left(\frac{\pi}{4}+2 \theta\right)\right)$ is equal to.
→
If the chord $y = mx + 1$ of the circle ${x^2} + {y^2} = 1$ subtends an angle of measure ${45^o}$ at the major segment of the circle then value of $m$ is
→
If the numbers $a,\;b,\;c,\;d,\;e$ form an $A.P.$, then the value of $a - 4b + 6c - 4d + e$ is
→
If the straight line through the point $P(3,\,4)$ makes an angle $\frac{\pi }{6}$with the $x$-axis and meets the line $12x + 5y + 10 = 0$ at $Q$, then the length $PQ$ is
→
The point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ lies on the line
→
A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $\frac{1}{4}$. Three stones $A , B$ and $C$ are placed at the points $(1,1),(2,2)$ and $(4,4)$ respectively. Then which of these stones is $/$ are on the path of the man ?
→
${\log _{\frac{1}{8}\cos e{c^2}\frac{\pi }{8}}}\,{\sin ^2}\frac{{3\pi }}{8}$ equals to
→
If $A = 130^\circ $ and $x = \sin A + \cos A,$ then
→
Identify the statement(s) which is/are True.
→