List of top Mathematics Questions on Differential Calculus asked in KCET

If $y = \sqrt{\tan x + y}$, then $\frac{dy}{dx} = $

The second order derivative of $\sec^{-1}\left(\frac{1}{2x^2 - 1}\right)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $0<x<\frac{1}{\sqrt{2}}$ is

If $\sqrt{x} \sqrt[3]{y} = (x + y)^n$ and $x\frac{dy}{dx} - y = 0$, then $n =$

The distance ‘s’ in meters travelled by a particle in ‘t’ seconds is given by s = \(\frac{2t^3}{3}-18t+\frac{5}{3}.\) The acceleration when the particle comes to rest is

An enemy fighter jet is flying along the curve given by y = x² + 2. A soldier is placed at (3, 2) wants to shoot down the jet when it is nearest to him. Then the nearest distance is

A particle starts form rest and its angular displacement (in radians) is given by \(\theta=\frac{t^2}{20}+\frac{t}{5}\). If the angular velocity at the end of t = 4 is k, then the value of 5k is

If y = (x - 1)² (x - 2)³ (x - 3)⁵ then \(\frac{dy}{dx}\) at x = 4 is equal to

For constant a, \(\frac{d}{dx}\)(x^x + x^a+ a^x + a^a) is

If a and b are fixed non-zero constants, then the derivative of \(\frac{a}{x^4}-\frac{b}{x^2}\) + cos x is ma + nb - p where

The curve passing through the point (1, 2) given that the slope of the tangent at any point (x, y) is \(\frac{2x}{y}\) represents

The maximum value of \(\frac{\log_ex}{x}\), if x > 0 is

If y = 2xⁿ⁺¹ + \(\frac{3}{x^n}\) then x²\(\frac{d^2y}{dx^2}\) is

If 2^x + 2^y = 2^x+y, then \(\frac{dy}{dx}\) is