List of top Mathematics Questions on Differentiability asked in KEAM

If x=sin−1(3t−4t3)x=sin^{-1}\left(3t-4t^{3}\right) and y=cos−1(1−t2)y=cos^{-1}\left(\sqrt{1-t^{2}}\right), then dydx\frac{dy}{dx} is equal to
If f(x)=2x+42xf(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}} , then f′(2)f'(2) is equal to
If y=sin⁡−1(3x−4x3)+cos⁡−1(4x3−3x) y={{\sin }^{-1}}(3x-4{{x}^{3}})+{{\cos }^{-1}}(4{{x}^{3}}-3x) +tan⁡−1(e), +{{\tan }^{-1}}(e), then dydx \frac{dy}{dx} is equal to
If y=tan⁡−1(cos⁡x1+sin⁡x), y={{\tan }^{-1}}\left( \frac{\cos x}{1+\sin x} \right), then dydx \frac{dy}{dx} is equal to
If f(x)=(x2)10,then f(1)+f′(1)⌊1+f(1)⌊2+f′(1)⌊3+…+f(10)(1)⌊10 \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 y2=100tan⁡−1x+45sec−1x,y^{2}=100 \tan^{-1}x+45 sec^{-1}x , then dydx=\frac{dy}{dx}=
If y=sin⁡−11−x, y={{\sin }^{-1}}\sqrt{1-x}, then dydx \frac{dy}{dx} is equal to
The derivative of sin⁡−1(2x1−x2) {{\sin }^{-1}}(2x\sqrt{1-{{x}^{2}}}) with respect to sin⁡−1(3x−4x3) {{\sin }^{-1}}(3x-4{{x}^{3}}) is
The functions f,gf , g and hh satisfy the relations f′(x)=g(x+1)f ^{'}\left(x\right)=g\left(x+1\right). Then f"(2x)f ^{"}\left(2x\right) is equal to
If y=xx+1+x+1x,y=\frac{x}{x+1}+\frac{x+1}{x}, then d2ydx2\frac{d^{2}y}{dx^{2}} at x=1x=1 is equal to