List of top Mathematics Questions on Differentiation asked in TS EAMCET

If \( f(x) = \begin{cases} x^2 \cos\left(\frac{\pi}{x}\right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then at \( x = 0 \), \( f(x) \) is

If $y=f(x)^{g(x)}$ and $\frac{dy}{dx} = y[H(x)f'(x)+G(x)g'(x)]$, then $\int \frac{G(x)H(x)f'(x)}{g(x)}dx =$

If $x=t-\sin t, y=1-\cos t$ and $\frac{d^2y}{dx^2}=-1$ at $t=K, K>0$, then $\lim_{t \to K} \frac{y}{x} =$

The set of all values of x for which $f(x) = ||x|-1|$ is differentiable is

If $y = \sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+\sqrt{\log(x^2+1)+...}}}$, $|x|<1$, then $\frac{dy}{dx} =$

If $x = \sqrt{1-\tan y}$, then $\frac{dy}{dx} =$

If $y = \text{Sec}^{-1}x$, then $\frac{d^2y}{dx^2} =$

If $x = \sin 2\theta \cos 3\theta$, $y = \sin 3\theta \cos 2\theta$, then $\frac{dy}{dx} =$

If $f(x) = \log_{(x-1)^2}(x^2-3x+2)$, $x \in \mathbb{R}-[1,2]$ and $x\neq0$, then $f'(3)=$

If $y=(1-x^2)\text{Tanh}^{-1}x$ then $\frac{d^2y}{dx^2}=$

The values of x at which the real valued function $f(x)=7|2x+1|-19|3x-5|$ is not differentiable is

If $y^3=x$ then the value of $\frac{dy}{dx}$ at $x=1$ is