JEE MAIN Differentibility Previous Year Questions (PYQs) – Page 1 of 3

The value of $\log_{e}2 \, \dfrac{d}{dx}\!\big(\log_{\cos x} \csc x\big)$ at $x=\tfrac{\pi}{4}$ is:

Let f : R $ \to $ R be a function defined by f(x) = max {x, x²}. Let S denote the set of all points in R, where f is not differentiable.Then :

Let $S={(\lambda,\mu)\in\mathbb{R}\times\mathbb{R}: f(t)=(\lvert\lambda\rvert e^{\lvert t\rvert}-\mu)\cdot\sin(2\lvert t\rvert),\ t\in\mathbb{R},\text{ is a differentiable function}}$. Then $S$ is a subset of :

Let $K$ be the set of all real values of $x$ where the function $f(x)=\sin|x|-|x|+2(x-\pi)\cos|x|$ is not differentiable. Then the set $K$ is equal to:

Let $S={t\in\mathbb{R}: f(x)=|x-\pi|,(e^{|x|}-1)\sin|x|\ \text{is not differentiable at }t}$. Then the set $S$ is equal to

Let $S$ be the set of all points in $(-\pi,\pi)$ at which the function $f(x)=\min\{\sin x,\cos x\}$ is not differentiable. Then $S$ is a subset of which of the following?

$ \text{The number of points where the function } f:\mathbb{R}\to\mathbb{R},\quad f(x)=|x-1|\cos|x-2|\sin|x-1|+(x-3),|x^{2}-5x+4|,\ \text{is NOT differentiable, is:} $

Let f, g : R $\to$ R be two real valued functions defined as $f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x < 0} \cr {{e^x}} & , & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^2} + {k_1}x} & , & {x < 0} \cr {4x + {k_2}} & , & {x \ge 0} \cr } } \right.$, where k₁ and k₂ are real constants. If (gof) is differentiable at x = 0, then (gof) ($-$ 4) + (gof) (4) is equal to :

The function $f(x)=2x+3\,x^{1/3},\ x\in\mathbb{R},$ has

Let the functions f : R $ \to $ R and g : R $ \to $ R be defined as :$f(x) = \left\{ {\matrix{ {x + 2,} & {x < 0} \cr {{x^2},} & {x \ge 0} \cr } } \right.$ and $g(x) = \left\{ {\matrix{ {{x^3},} & {x < 1} \cr {3x - 2,} & {x \ge 1} \cr } } \right.$ Then, the number of points in R where (fog) (x) is NOT differentiable is equal to :