If $y = x \sin x$, then $y_2 = \dfrac{d^2y}{dx^2}$ equals:
A$-x\sin x$
B$x\cos x$
C$2\cos x - x \sin x$
D$\cos x + \sin x$
Answer & Solution
Correct answer: C. $2\cos x - x \sin x$
$y' = \sin x + x\cos x$. $y'' = \cos x + \cos x + x(-\sin x) = 2\cos x - x\sin x$.
Related questions
$\dfrac{d}{dx}\left[\cos^{-1}\left(\dfrac{1-x^2}{1+x^2}\right)\right]$ for $x > 0$ equals:If $f(x) = e^{ax} in(bx)$, then $f''(x) + a^2 f(x)$ equals:If $f(x) = x^3 - 3x$, the values of $x$ where $f'(x) = 0$ are:If $y_n$ denotes the $n$-th derivative of $y = in x$, then $y_n = $:If $y = \tan^{-1}\left(\dfrac{ qrt{1+x^2} - 1}{x}\right)$, then $\dfrac{dy}{dx}$ equals:If $f(x) = |x - 1| + |x - 3|$, then $f'(2)$ equals:If $y = e^x \cos x$, then $\dfrac{d^2 y}{dx^2} - 2\dfrac{dy}{dx} + 2y$ equals:Given $x = a(\theta - in\theta)$, $y = a(1 - \cos\theta)$ (cycloid). Then $\dfrac{dy}{dx}