List of top Mathematics Questions on Continuity and differentiability asked in AP ECET Ceramic Tech

If \[ f(x)= \begin{cases} 4(5^x), & x 8k+x, & x\geq 0 \end{cases} \] then \(f'(-1)=\)

If \[ 2^x+2^y=2^{x+y}, \] then \[ \frac{dy}{dx}= \]

If \[ y+\sin^{-1}(1-x^2)=e^x, \] then \[ \frac{dy}{dx}= \]

If \[ z=x^2y^3+e^y\sin x, \] then \[ \frac{\partial^2 z}{\partial x\partial y}= \]

If \[ y=\frac{a\cos x+b\sin x+c}{\sin x}, \] then \[ \frac{dy}{dx}= \]

If \[ y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots\infty}}}, \] then \[ \frac{dy}{dx}= \]

The derivative of \(x^x\) with respect to \(x\) is

\(\displaystyle \frac{d}{dx}\left(\tan^{-1}\frac{x}{a}\right)=\)

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots\infty}}}\), then \(\displaystyle \frac{dy}{dx}=\)

The derivative of \(x^x\) with respect to \(x\) is

\(\displaystyle \frac{d}{dx}\left(\tan^{-1}\frac{x}{a}\right)=\)

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots\infty}}}\), then \(\displaystyle \frac{dy}{dx}=\)