List of top Mathematics Questions on Second Order Derivative asked in COMEDK UGET

The second derivative of \( \sin 3x \cos 5x \) is:

If $y=e^{mx}\sin(nx)$, then the value of \[ \frac{d^2y}{dx^2}-2m\frac{dy}{dx}+(m^2+n^2)y \] is:

If $\log y=\log(\sin x)-x^2$, then \[ \frac{d^2y}{dx^2}+4x\frac{dy}{dx}+4x^2y= \]

If \( y = x + e^x \) then \( \frac{d^2 x}{dy^2} = \)

If \[ y = (\sin^{-1} x)^2 + (\cos^{-1} x)^2, \] then \[ (1 - x^2) \frac{d^2y}{dx^2} - x \frac{dy}{dx} = \]