Limits and Deri...

If $y=\sec(\tan^{-1}x)$, then $\displaystyle\frac{dy}{dx}$ at $x=1$ is equal to.

If $\displaystyle \lim _{ n\rightarrow \infty  }{ \cfrac { n.{ 3 }^{ n } }{ n{ \left( x-2 \right)  }^{ n }+n.{ 3 }^{ n+1 }-{ 3 }^{ n } }  } =\cfrac { 1 }{ 3 }$, then the range of $x$ is (When $n\in N$)

If $y = |\cos x| + |\sin x|$, then $\dfrac {dy}{dx}$ at $x = \dfrac {2\pi}{3}$ is

The derivative of $f\left( \tan { x }  \right)$ with respect to $g(\sec x)$ at $\quad x=\cfrac { \pi  }{ 4 }$, where $f'(1)=2;\quad g'(\sqrt { 2 } )=4$ is

If $|x| < 1$, then $\dfrac{d}{dx}\left[1+\dfrac{p}{q}x+\dfrac{p(p+q)}{2!}\left(\dfrac{x}{q}\right)^2+\dfrac{p(p+q)(p+2q)}{3!}\left(\dfrac{x}{q}\right)^3....\infty\right]=$

$\lim _{ x\rightarrow 3 }{ \left( { x }^{ 3 }-4 \right) /\left( x+1 \right)  } =$

Differentiate the following w.r.t. $x$.
$\sin x\ log x$.

Differentiate the following w.r.t. $x$.
$\tan^{3}x$.

Given $y=\dfrac {3}{x}, \dfrac {dy}{dx}=$

Differentiate the following w.r.t. $x$.
$\tan x^{2}$.