List of top Mathematics Questions on Second Order Derivative asked in KEAM

If $y = 4\sqrt{x}$, then $\frac{d^2y}{dx^2} =$}

Let $y = 4e^{-x} - 2e^{-2x} - e^{-3x}, x \in \mathbb{R}$. If $\frac{d^2y}{dx^2} = e^{\alpha x}(4e^{2x} - 8e^x - 9)$ for all $x$, then the value of the constant $\alpha$ is

If $f(x)=(2x+3)e^{5x}$, then $f^{\prime\prime}(1)-10f^{\prime}(1)$ is equal to

If $y = e^{-x^2}$, then $\dfrac{d^2y}{dx^2} + 2x\dfrac{dy}{dx}$ is equal to:

Find \(\int_{-1}^{1} \frac{\log(1 + |x|)}{1 + |x|} \, dx\)

If \( y=(5x-2)e^x \), then \( \dfrac{d^2y}{dx^2} \) is equal to

If \(y = (x - 1)\log_{e}(x - 1)\), then \(\frac{d^{2}y}{dx^{2}}\) at \(x = 3\) is

Let $f(x)=\frac{5}{2}x^{2}-e^{x}$. Then the value of $c$ such that $f''(c)=0$ is

If \( x = A\cos 4t + B\sin 4t \), then \( \frac{d^2x}{dt^2} = \)

If \( y = \frac{x}{x+1} + \frac{x+1}{x} \), then \( \frac{d^2y}{dx^2} \) at \( x=1 \) is equal to