If y = x^ ln , x , then dy/dx equals :- - Vidyadip

MCQ

If $y = x^{ln\, x}$, then $dy/dx$ equals :-

A
$ln\, x . x^{ln\, x-1}$
✓
$x^{ln \,x-1} . 2ln\, x$
C
$x\, ln\, (ln\, x)$
D
$1/(x\, ln\, x) . x^{ln\, x-1}$

✓

Answer

Correct option: B.

$x^{ln \,x-1} . 2ln\, x$

b

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

For the system of linear equations

$2 x-y+3 z=5$

$3 x+2 y-z=7$

$4 x+5 y+\alpha z=\beta$

Which of the following is NOT correct ?

If $s$ is the sum of an infinite $G.P.$, the first term $a$ then the common ratio $r$ given by

The area enclosed by the curves $y^2+4 x=4$ and $y-2 x=2$ is :

The relation "less than" in the set of natural numbers is

Let the first three terms $2, p$ and $q$, with $q \neq 2$, of a $G.P.$ be respectively the $7^{\text {th }}, 8^{\text {th }}$ and $13^{\text {th }}$ terms of an $A.P.$ If the $5^{\text {th }}$ term of the $G.P.$ is the $\mathrm{n}^{\text {th }}$ term of the $A.P.$, then $\mathrm{n}$ is equal to

$\int_{}^{} {\frac{1}{{{x^2}}}{{(2x + 1)}^3}} dx = $

$ \text { If } S(x)=(1+x)+2(1+x)^2+3(1+x)^3+\ldots . $

$ +60(1+x)^{60}, x \neq 0 \text {, and }(60)^2 S(60)=a(b)^b+b$ where $a, b N$, then $(a+b)$ equal to...............

If $\left[ {a \times b\;\;b \times c\;\;c \times a} \right] = \alpha \;{\left[ {a\;\;b\;\;c} \right]^2}$ then $\lambda$ is equal to

The remainder when $\left((64)^{(64)}\right)^{(64)}$ is divided by 7 is equal to

If $f(x)\, = {\cot ^{ - 1}}\left( {\frac{{3x - {x^3}}}{{1 - 3{x^2}}}} \right)$ and $g(x) = {\cos ^{ - 1}}\left( {\frac{{1 - {x^2}}}{{1 + {x^2}}}} \right)$, then $\mathop {\lim }\limits_{x \to a} \frac{{f(x) - f(a)}}{{g(x)\, - g(a)}},$ $0 < \,a < \frac{1}{2}$ is