List of top Mathematics Questions on Second Order Derivative

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:

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

The second-order derivative of which of the following functions is $5^x$?

If $t = e^{2x}$ and $y = \ln(t^2)$, then $\frac{d^2 y}{dx^2}$ is:

If \[ x = \sqrt{e^{\sin^{-1} t}} \quad \text{and} \quad y = \sqrt{e^{\cos^{-1} t}}, \] then find \[ \frac{d^2 y}{dx^2}. \]

Let $f$ be a twice differentiable function on $R$. 
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$ 
then $(2 a+1)^5 a^2$ is equal to ______.

If \[ y = \frac{x}{x+1} + \frac{x+1}{x}, \] then \[ \frac{d^2 y}{dx^2} \text{ at } x = 1 \text{ is equal to:} \]

Let \(y = e^{2x}\). Then \(\frac{d^2 y}{dx^2} \cdot \frac{d^2 x}{dy^2}\) is: