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

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