List of top Mathematics Questions on Differentiability asked in KEAM

If $f(x)=\sin(|x|)-|x|,x\in\mathbb{R}$, then $f$ is ________.

The function $f(x)=|x^{2}-3x+2|,x\in\mathbb{R}$ is not differentiable at ________.

Find the minimum of the function \[ f(x) = |x+2| \]

Let $f(x) = \int_{1}^{x} \sin^2 \left(\frac{t}{2}\right) dt$. Then the value of $\lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x}$ is equal to:

Let \( f(x) = \int_{1^{x} \sin^2 \left( \frac{t}{2} \right) dt \). Then the value of \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:}

Let \( f(x) = \int_{1^{x} \sin^2 \left( \frac{t}{2} \right) dt \). Then the value of \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:}

If f(x)=$ \left(\frac{x}{2}\right)^{10}, then\, f \left(1\right)+\frac{f '\left(1\right)}{\lfloor1}+\frac{f \left(1\right)}{\lfloor2}+\frac{f '\left(1\right)}{\lfloor3}+\ldots+\frac{f ^{\left(10\right)}\left(1\right)}{\lfloor10}$ is equal to

If $y^{2}=100 \tan^{-1}x+45 sec^{-1}x ,$ then $\frac{dy}{dx}=$

If $x=sin^{-1}\left(3t-4t^{3}\right)$ and $y=cos^{-1}\left(\sqrt{1-t^{2}}\right)$, then $\frac{dy}{dx}$ is equal to

If $f(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}}$ , then $f'(2) $ is equal to

If $ y={{\sin }^{-1}}(3x-4{{x}^{3}})+{{\cos }^{-1}}(4{{x}^{3}}-3x) $ $ +{{\tan }^{-1}}(e), $ then $ \frac{dy}{dx} $ is equal to

If $ y={{\tan }^{-1}}\left( \frac{\cos x}{1+\sin x} \right), $ then $ \frac{dy}{dx} $ is equal to

If $ y={{\sin }^{-1}}\sqrt{1-x}, $ then $ \frac{dy}{dx} $ is equal to

The derivative of $ {{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}}) $ with respect to $ {{\sin }^{-1}}(3x-4{{x}^{3}}) $ is

The functions $f , g$ and $h$ satisfy the relations $f ^{'}\left(x\right)=g\left(x+1\right)$. Then $f ^{"}\left(2x\right)$ is equal to

If $y=\frac{x}{x+1}+\frac{x+1}{x},$ then $\frac{d^{2}y}{dx^{2}} $ at $x=1$ is equal to