List of top Mathematics Questions on Second Order Derivative asked in MHT CET

If \( y = \cos^{-1} x \), find \( \frac{d^2y}{dx^2} \) in terms of \( y \).

For \(n\in\mathbb{N}\), if \[ y=ax^{n+1}+bx^{-n}, \] then \[ x^2\frac{d^2y}{dx^2} \] is equal to:

For \(n\in\mathbb{N}\), if \[ y=ax^{n+1}+bx^{-n}, \] then \[ x^2\frac{d^2y}{dx^2} \] is equal to:

If $x = a \sin t - b \cos t$ and $y = a \cos t + b \sin t$, and it is given that $\frac{d^2y}{dx^2} = 0$, then:

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

If $y = \tan^{-1}\left[\frac{\log\left(\frac{e}{x^2}\right)}{\log(ex^2)}\right] + \tan^{-1}\left[\frac{3 + 2\log x}{1 - 6\log x}\right]$, then $\frac{d^2y}{dx^2} = $

If \( y = 2 \sin x + 3 \cos x \) and \( y + A \frac{d^2 y}{dx^2} = B \), then the values of \( A, B \) are respectively

If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:

A wire of length 20 units is divided into two parts such that the product of one part and the cube of the other part is maximum. The product of these parts is: