Continuity and ...

The derivate of $$\tan^{-1}[\dfrac {\sin x}{1+\cos x}]$$ with respect to $$\tan^{-1}[\dfrac {\cos x}{1+\sin x}]$$ is

$$S$$ be the set in which function defined by $$f(x)=\sin |x|- |x|+2(x-\pi)\cos |x|$$ is  differtentiable then no of element in $$S$$ is

If  $$y = \sin ^ { - 1 } \dfrac { 2 x } { 1 + x ^ { 2 } } ,$$  then which of the following is not correct ?

If $$f(x)$$ is differentiable function and $$f(1) = \sin 1, f(2) = \sin 4, f(3) = \sin 9$$, then the minimum number of distinct solutions of equation $$f'(x) = 2x \,\cos \,x^2$$ in $$(1, 3)$$ is

If $$y = {\cot ^{ - 1}}\left[ {\dfrac{{\sqrt {1 + \sin x}  + \sqrt {1 - \sin x} }}{{\sqrt {1 + \sin x}  - \sqrt {1 - \sin x} }}} \right]\;then\;\dfrac{{dy}}{{dx}}\;is\;equal\;to\;$$ 

If $$f\left(x\right)$$ is a differentiable function in the interval $$\left(0,\infty\right)$$ such that $$f\left(1\right)=1$$ and  $$\lim_{t\rightarrow x}\dfrac{t^{2}f\left(x\right)-x^{2}f\left(t\right)}{t-x}=1$$, for each $$x>0$$, then $$f\left(\dfrac{3}{2}\right)$$ is equal to:

Let $$f\left( x \right)=x\left| x \right| ,g\left( x \right)=sinx$$ and $$h\left( x \right) =\left( gof \right) \left( x \right) .$$ Then

Let f be a differentiable function satisfying the condition  $$f\left( \dfrac { x }{ y }  \right) =\dfrac { f\left( x \right)  }{ f\left( y \right)  } ,$$ for all x, y$$\left( \neq 0 \right) \epsilon R$$ and f(y)$$\neq $$0. If f'(1)=2, then f'(x) is equal to 

The value of $$f(4)$$ is

Let f be a differentiable function satisfying the relation f(xy) = xf(y) - 2xy+yf(x) (where x,y > 0) and f(1) = 3, then