List of top Mathematics Questions on Differentiation asked in COMEDK UGET

If \(y=\sqrt{\frac{x}{a}}+\sqrt{\frac{a}{x}}\), then \(2xy\frac{dy}{dx}\) is equal to

The general solution of the differential equation $ x \frac{dy}{dx} = y + x \tan\left(\frac{y}{x}\right) $

The sum of the order and degree of the differential equation $ \left( \frac{d^5y}{dx^5} \right) + 4 \left( \frac{d^4y}{dx^4} \right) + \left( \frac{d^3y}{dx^3} \right) = x^2 - 1 $

The turning point of the function $ y = \frac{ax-b}{(x-1)(x-4)} $ at the point $ P(2, -1) $ is

What is the nature of the function $ f(x) = x^3 - 3x^2 + 4x $ on real numbers?

If $ y = \sin^{-1} \left( \frac{5x + 12\sqrt{1 - x^2}}{13} \right) $ then $ \frac{dy}{dx} $ equals

If $ \frac{dy}{dx} = y + 3 \quad \text{and} \quad y(0) = 2, \quad \text{then} \quad y(\log 2) \text{ is equal to:} $

The general solution of the differential equation $ (1 + \tan y)(dx - dy) + 2x \, dx \, dy = 0 $

If $ y = \sqrt{\sin x + y} $, then find $ \frac{dy}{dx} $ at $ x = 0, y = 1 $.

If $ f(x) = \begin{cases} x, & 0 \leq x \leq 1 \\ 2x - 1, & x > 1 \end{cases} $, then:

If $ y = f(x), \, p = \frac{dy}{dx}, \, q = \frac{d^2 y}{dx^2}, \text{ then } \frac{d^2 x}{dy^2} \text{ is equal to } $

The slope of the tangent to the curve, $ y = x^2 - xy $ at $ (1, \frac{1}{2}) $ is