If f(x) = a ( x), then x^2 f''(x) + xf'(x) = . . . - Vidyadip

MCQ

If $f(x) = a\sin (\log x)$, then ${x^2}f''(x) + xf'(x) = . . . $

A
$f(x)$
✓
$ - f(x)$
C
$0$
D
$1$

✓

Answer

Correct option: B.

$ - f(x)$

b
(b) $f(x) = a\sin (\log x)$

Differentiating w.r.t. $x$ of $y$, we get $f(x) = a\cos (\log x) \frac{1}{x} $

Again $f''\,(x) = - \frac{1}{{{x^2}}}a\cos (\log x) - \frac{1}{{{x^2}}}a\sin (\log x)$

$ \Rightarrow {x^2}f''(x) = - [a\cos (\log x) + a\sin (\log x)]$

Now ${x^2}f''(x) + xf'(x) = - a\sin (\log x) = - f(x)$.

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

Suppose the sequence $a_1, a_2, a_3, \ldots$ is a n arithmetic progression of distinct numbers such that the sequence $a_1, a_2, a_4, a_8, \ldots$ is a geometric progression. The common ratio of the geometric progression is

If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is

If polynomial $P\left( x \right) = {x^2} + ax + b$ has factors$\left( {x - a} \right)\left( {x - b} \right)$,$a$,$b \in R$ then value of $P(2)$ is

What are the minimum and maximum values of the function ${x^5} - 5{x^4} + 5{x^3} - 10$

$\mathop {\lim }\limits_{x \to \infty } \frac{{{{(2x + 1)}^{40}}{{(4x - 1)}^5}}}{{{{(2x + 3)}^{45}}}} = $

Let $\mathrm{n}>2$ be an integer. Suppose that there are $n$ Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is $99$ times the number of blue lines, then the value of $n$ is

One coin is thrown $100$ times. The probability of coming tail in odd number

Let mininmm $m$ , $(m\in Z^+)$ is define as power of a square matrix $'A'$ such that $A^m = I$ . If $A^5 = I$ and $ABA^{-1} = B^2$ . then power of matrix $B$ is between

Let $\overrightarrow{ u }, \overrightarrow{ v }$ and $\overrightarrow{ w }$ be vectors in three-dimensional space, where $\overrightarrow{ u }$ and $\overrightarrow{ v }$ are unit vectors which are not perpendicular to each other and $\overrightarrow{ u } \cdot \overrightarrow{ w }=1, \overrightarrow{ v } \cdot \overrightarrow{ w }=1, \overrightarrow{ w } \cdot \overrightarrow{ w }=4$

If the volume of the parallelopiped, whose adjacent sides are represented by the vectors $\overrightarrow{ u }, \overrightarrow{ v }$ and $\overrightarrow{ w }$ , is $\sqrt{2}$, then the value of $|3 \vec{u}+5 \vec{v}|$ is. . . . .

The derivative of $f(x) = x|x|$ is