If y = x. e^ ( x + x^2 ) , then dy dx = - Vidyadip

MCQ

If $y = \log x.{e^{(\tan x + {x^2})}},$ then ${{dy} \over {dx}} = $

A
${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x + x)\log x} \right]$
B
${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x - x)\log x} \right]$
✓
${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x + 2x)\log x} \right]$
D
${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x - 2x)\log x} \right]$

✓

Answer

Correct option: C.

${e^{(\tan x + {x^2})}}\left[ {{1 \over x} + ({{\sec }^2}x + 2x)\log x} \right]$

c
(c) $y = \log x.{e^{(\tan x + {x^{2)}}}}$

$\therefore \frac{{dy}}{{dx}} = {e^{(\tan x + {x^2})}}.\frac{1}{x} + \log x.{e^{(\tan x + {x^2})}}({\sec ^2}x + 2x)$

$ = {e^{(\tan x + {x^2})}}\left[ {\frac{1}{x} + ({{\sec }^2}x + 2x)\log x} \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 locus of the poles of normal chords of an ellipse is given by

Let $\theta$ be the acute angle between the tangents to the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{1}=1$ and the circle $x^{2}+y^{2}=3$ at their point of intersection in the first quadrant. Then $\tan \theta$ is equal to :

Two consecutive sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0.$ If the equation to one diagonal is $11x + 7y = 9,$ then the equation of the other diagonal is

$\int_0^{\pi /4} {} \sec x\log (\sec x + \tan x)\,dx = $

A natural number is selected at random from the set $\{1 \leq x \leq 100\}.$ The probatility that number satisfies the inequation $x^2 -13x \leq 30$ is :-

Let $S=\{1,2,3, \ldots, 100\}$. Suppose $b$ and $c$ are chosen at random from the set $S$. The probability that $4 x^2+b x+c$ has equal roots is

The differential equation $\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}} + \sin y + {x^2} = 0$ is of the following type

A rectangle is inscribed in a circle with a diameter lying along the line $3y = x + 7$ . If the two adjacent vertices of the rectangle are $(-8, 5)$ and $(6, 5)$ then the area of the rectangle (in $sq. units$) is

If $x{e^{xy}} = y + {\sin ^2}x$, then at $x = 0,{{dy} \over {dx}} = $

Let ${\left( {5\,\, + \,\,2\,\sqrt 6 } \right)^n} = p + f$ where $n \in N $ and $p \in N$ and $0 < f < 1$ then the value of, $f^2 - f + pf - p$ is