Continuity and ...

If $$x=a\cos ^{ 4 }{ t } ,y=b\ cosec^{ 4 }{ t } $$, then $$\cfrac { dx }{ dy } $$ at $$t=\cfrac { 3\pi  }{ 4 } $$

If $$y = \tan ^ { - 1 } \left( \cot \left( \dfrac { \pi } { 2 } - x \right) \right) ,$$ then $$\dfrac { d y } { d x } =$$

If $$y=\tan^{-1}\left(\dfrac{2^{x+1}}{1+2^{2x}}\right) $$ then $$\dfrac{dy}{dx}$$ at $$x=0$$ is

If $$y=\log \sin x$$ find $$x$$ if $$y=0$$

If $$f ( x ) =  \tan x$$ and $$f$$ is inverse of $$g ,$$ then $$g ^ { \prime } ( x )$$is equal to

Find the values of a and b so that the function $$f(x)=\left\{\begin{matrix} x^2+3x+a, & if & x\leq 1\\ bx+2, & if & x > 1\end{matrix}\right.$$ is differentiable at each $$x\in R$$.

The set of points where the functions f given by $$f(x)=|x-3|\cos x$$ differentiable is

lf $$f(x)=\sin^{6}x+\cos^{6}x$$ then $$f''(x)=$$

Let $$f(x)$$ be differentiable function such that $$f\left (\displaystyle \frac{x+y}{1-xy}\right)=f(x)+f(y)\forall x$$ and $$y$$. lf $$ \displaystyle \lim_{x \rightarrow 0}\frac{f(x)}{x}=\frac{1}{3}$$, then $$f(1)$$ equals

$$\displaystyle \mathrm{A}:\dfrac{d}{dx}(\sin x)\ at\ x=\frac{\pi}{2}$$