If y = x^x , then dy dx = - Vidyadip

MCQ

If $y = {x^x}$, then ${{dy} \over {dx}} = $

✓
${x^x}\log ex$
B
${x^x}\left( {1 + {1 \over x}} \right)$
C
$(1 + \log x)$
D
${x^x}\log x$

✓

Answer

Correct option: A.

${x^x}\log ex$

a
(a) $y = {x^x}$

Taking $\log $ on both sides, ==> $\log y = x\log x$

Differentiating with respect to $x,$ we get

==> $\frac{1}{y}\frac{{dy}}{{dx}} = 1 + \log x$;

$\therefore \frac{{dy}}{{dx}} = {x^x}(1 + \log x) = {x^x}\log ex$.

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

For $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$, then $14 A^{-1}$ is given by

The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.

	Number of cars manufactured
Colour	Vento	Creta	WagonR
Red	65	88	93
White	54	42	80
Black	66	52	88
Sliver	37	49	74

What was the total number of black cars manufactured?

The vector equation of the plane passing through $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}},$ is $\vec{\text{r}}=\alpha\vec{\text{a}}+\beta\vec{\text{b}}+\gamma\vec{\text{c}}$, provided that,

$\alpha+\beta+\gamma=0$
$\alpha+\beta+\gamma=1$
$\alpha+\beta=\gamma$
$\alpha^2+\beta^2+\gamma^2=1$

If $\frac{{dy}}{{dx}} = 1 + x + y + xy$ and $y( - 1) = 0,$ then function $y$ is

If the shortest distance between the straight lines $3(x-1)=6(y-2)=2(z-1)$ and $4(\mathrm{x}-2)=2(\mathrm{y}-\lambda)=(\mathrm{z}-3), \lambda \in \mathrm{R}$ is $\frac{1}{\sqrt{38}}$, then the integral value of $\lambda$ is equal to :

The values of the determinant $\left| {\,\begin{array}{*{20}{c}}1&{\cos (\alpha - \beta )}&{\cos \alpha }\\{\cos (\alpha - \beta )}&1&{\cos \beta }\\{\cos \alpha }&{\cos \beta }&1\end{array}\,} \right|$ is

The solution of differential equation $\frac{{dy}}{{dx}} + y = 1$ is

Let $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ be a thrice differentiable function such that $f(0)=0, f(1)=1, f(2)=-1, f(3)=2$ and $f(4)=-2$. Then, the minimum number of zeros of $\left(3 f^{\prime} f^{\prime \prime}+f f^{\prime \prime \prime}\right)(x)$ is....................

A particle starts at the origin and moves along the $x$-axis in such a way that its velocity at the point $(x, 0)$ is given by the formula $\frac{{dx}}{{dt}} = {\cos ^2}\pi x.$ Then the particle never reaches the point on

Number of points of discontinuity of the function $f\left( x \right) = \sin \left( {\left\{ {{2^x} + \left[ {{2^x}} \right] + \left[ {{3^{ - x}}} \right]} \right\}} \right)$ for $x \in \left[ {0,4} \right]$ is (where [.] and {.} denotes greatest integer and fractional part function respectively)