Download App

Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability1 Mark
MCQ
If $y=x \log x$ then value of $\frac{d^2 y}{d x^2}$ :
  • A
    $\frac{1}{1+x}$
  • ✓
    $\frac{1}{x}$
  • C
    $\log (1+x)$
  • D
    $1+\log x$
✓

Answer

Correct option: B.
$\frac{1}{x}$
(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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\lambda $ for which the system of equations $2x - y - z = 12,$ $x - 2y + z = - 4,$ $x + y + \lambda z = 4$ has no solution is
→
$3 x^2-6 x+5$ is an increasing function, if
→
$\int\limits^1_0\sqrt{\text{x}(1-\text{x})}\text{ dx}$ equals:

  1. $\frac{\pi}{2}$

  2. $\frac{\pi}{4}$

  3. $\frac{\pi}{6}$

  4. $\frac{\pi}{8}$

→
Choose the correct answer from the given four options.

For any two matrices A and B, we have:

  1. $\text{AB}=\text{BA}$

  2. $\text{AB}\neq\text{BA}$

  3. $\text{AB}=\text{O}$

  4. None of the above.

→
Find definite integral of $\int_a^b {\frac{1}{x}dx} $
→
A pack of playing cards was found to contain only 51 cards. If the first 13 cards which are examined are all red, then the probability thatthe missing card is black, is:

  1. $\frac13$

  2. $\frac23$

  3. $\frac12$

  4. $\frac{^{25}{\text{C}_{13}}}{^{51}{\text{C}_{13}}}$

→
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is
→
$(a + b)\,.\,(b + c) \times (a + b + c) = $
→
Let $\vec{p}=2 \hat{i}+3 \hat{j}+k$ and $\vec{q}=\hat{i}+2 \hat{j}+k$ be two vectors. If $a$ vector $\vec{r}=(a \hat{i}+\beta \hat{j}+\gamma k)$ is perpendicular to each of the vectors $(\vec{p}+\bar{q})$ and $(\vec{p}-\vec{q})$, and $|\vec{r}|=\sqrt{3}$, then $|\alpha|+|\beta|+|\gamma|$ is equal to $.....$
→
Three forces $i + 2\,j - 3\,k,\,\,2\,i + 3\,j + 4\,k$ and $i - j + k$ are acting on a particle at the point $ (0, 1, 2)$ . The magnitude of the moment of the forces about the point $(1,\, - 2,\,0)$ is
→