Let $f$ be a differentiable function such that $f(1) = 2$ and $f'(x) = f(x)$ for all $x \in R$. If $h(x) = f(f(x))$,then $h'(1)$ is equal to

Let $f(x)$ be a differentiable function such that $f(1)=2$,$f(2)=6$ and $f(x+y)=f(x)+kxy+\frac{4}{3}y^2$ for all $x, y \in R$. Then $f(x)$ is:

Let $f: R \rightarrow R$ be defined by $f(x) = \log \left[e^x \left(\frac{x-2}{x+2}\right)^{3/4}\right]$. Find the value of $f'(0)$.

If $f(x) = \frac{x}{1+x}$ and $g(x) = f(f(x))$,then $g^{\prime}(x)$ is equal to

Let $f: R \rightarrow R$ satisfy the equation $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in R$ and $f(x) \neq 0$ for any $x \in R$. If the function $f$ is differentiable at $x=0$ and $f'(0)=3$,then $\lim_{h \rightarrow 0} \frac{1}{h}(f(h)-1)$ is equal to ....... .

If $y = (1 + x^{1/4})(1 + x^{1/2})(1 - x^{1/4})$,then $\frac{dy}{dx} = $