Continuity and ...

If $$y = Tan^{ -1 }\left(secx + tanx \right) then \dfrac { dy }{ dx }=$$

If $$x=\sin^ {-1}\left( \dfrac { 2\theta  }{ 1+{ \theta  }^{ 2 } }  \right),y=\sec^ {-1}\sqrt {1+\theta^ {2}}$$, then $$\dfrac {dy}{dx}=$$

If $$y={ tan }^{ -1 }\left( \frac { ax-b }{ bx+a }  \right)$$, the value of $$\frac { dy }{ dx } $$ is

Let $$f:[0,2]\rightarrow R$$ be a twice differentiable function such that $$f"(x)>0$$, for all $$x\in (0,2)$$ If $$\phi (x)=f(x)+f(2-x)$$, then $$\phi$$is:

Let $$f(x)=15-|x-10|; x\in R$$. Then the set of all values of x, at which the function, $$g(x)=f(f(x))$$ is not differentiable, is?

The set of points where the function $$f(x)=x|x|$$ is differentiable is?

If $$x=3\sin {t} ,\ y=3\cos {t} ,$$ find $$\dfrac {dy}{dx}$$ at $$t=\dfrac { \pi  }{ 3 } $$

Differentiate the following function with respect to x.
If for $$f(x)=\lambda x^2+\mu x+12$$, $$f'(14)=15$$ and $$f'(2)=11$$, then find $$\lambda$$ and $$\mu$$.

If $$f(9) = 9, f'(9) = 0$$, then $$\underset{x\to 9}{\lim} \dfrac{\sqrt{f(x)}-3}{\sqrt{x}-3}$$ is equal to 

Let $$f : R \rightarrow R$$ be a continuous function such that $$f(x^2) = f(x^3)$$ for all $$ x \in R$$. Consider the following statements.
I. f is an odd function.
II. f is an even function.
III. f is differentiable everywhere