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. $$x$$.
$$\tan x^{2}$$.