List of top Mathematics Questions on Differentiability asked in KCET

If \[ y = \frac{\cos x}{1 + \sin x} \] then:

Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 

 Choose the correct answer from the options given below:

The function f(x) is given by:

For x < 0:
f(x) = ex + ax

For x ≥ 0:
f(x) = b(x - 1)2


The function is differentiable at x = 0. Then,
If $2^x+2^y = 2^{x+y}$, then $\frac {dy}{dx}$ is
If $y = 2x^{n+1} + \frac {3}{x^n}$ ,then $x^2 \frac{d^2y}{dx^2}$ is
The function $ f (x) = x^2 + 2x - 5$ is strictly increasing in the interval
The derivative of $\cos^{-1} (2x^2 - 1)$ w.r.t $\cos^{-1} x$ is
The function $f(x) = [x]$, where $[x]$ denotes greatest integer function is continuous at
The derivative of $tan ^{-1}[\frac{Sin x}{1+ Cos x}]$ with respect to $tan^{-1}[\frac{Cos x}{1+Sin x}]$ is