Download App

Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability1 Mark
Question
If $y=x \log x$ then value of $\frac{d^2 y}{d x^2}$ :
✓

Answer

(B)
$\begin{aligned} & & y & =x \log x \\ \Rightarrow & & \frac{d y}{d x} & =x \cdot \frac{1}{x}+\log x \cdot 1 \\ \Rightarrow & & \frac{d y}{d x} & =1+\log x \\ \Rightarrow & & \frac{d^2 y}{d x^2} & =0+\frac{1}{x}=\frac{1}{x}\end{aligned}$

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 Continuity and Differentiability→Continuity and Differentiability — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{P(B)}=\frac{3}{5},\text{P}(\text{A}|\text{B})=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5},$ then $\text{P}(\text{B}|\overline{\text{A}})=$
→
If two angles of a triangle are $ \tan ^{ -1 }{ (2) }$ and $ \tan ^{ -1 }{ (3) }$, then the third angle is:
  1. $ \frac { \pi }{ 4 }$
  2. $ \frac { \pi }{ 5 }$
  3. $ \frac { \pi }{ 6 }$
  4. $ \frac { \pi }{ 8 }$
→
Choose the correct answer from the given four options.
The probability distribution of a discrete random variable X is given below:
$\text{X}$ $2$ $3$ $4$ $5$
$\text{P}(\text{X})$ $\frac{5}{\text{k}}$ $\frac{7}{\text{k}}$ $\frac{9}{\text{k}}$ $\frac{11}{\text{k}}$
The value of k is:
  1. 8.
  2. 16.
  3. 32.
  4. 48.
→
The area of the region bounded by the and the lines x = 2 and x = 3.
  1. $\frac{7}{2}\text{sq}.\text{units}$
  2. $\frac{9}{2}\text{sq}.\text{units}$
  3. $\frac{11}{2}\text{sq}.\text{units}$
  4. $\frac{13}{2}\text{sq}.\text{units}$
→
The general solution of differention eqution of the $e^x dy + (ye^x + 2x)dx = 0$ is :
→
$\int\frac{\text{x}^3}{\text{x}+1}$ is equal to:
  1. $\text{x}+\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{c}$
  2. $\text{x}+\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1-\text{x}|+\text{c}$
  3. $\text{x}+\frac{\text{x}^2}{2}-\frac{\text{x}^3}{3}-\log|1+\text{x}|+\text{c}$
  4. $\text{x}+\frac{\text{x}^2}{2}+\frac{\text{x}^3}{3}-\log|1+\text{x}|+\text{c}$
→
If $\left[\begin{array}{cc}2 a+b & a-2 b \\ 5 c-d & 4 c+3 d\end{array}\right]=\left[\begin{array}{cc}4 & -3 \\ 11 & 24\end{array}\right]$, then value of $a+b-c+2 d$ is
→
A set of values of decision variables that satisfies the linear constraints and non - negativity conditions of an L.P.P. is called its:
  1. Unbounded solution
  2. Optimum solution
  3. Feasible solution
  4. None of these
→
If the curve $ay + x^2 = 7$ and $x^3 = y,$ cut orthogonally at $(1, 1),$ then the value of $a$ is:
→
Consider the system of equations:
$a_1x + b_1y + c_1z = 0 , a_2x + b_2y + c_2z = 0 , a_3x + b_3y + c_3z = 0,$ if $\begin{vmatrix}\text{a}_1&\text{b}_1&\text{c}_1\\\text{a}_2&\text{b}_2&\text{c}_2\\\text{a}_3&\text{b}_3&\text{c}_3\end{vmatrix}=0$, then the system has
→