Derivative of $e^x$ with respect to $\sqrt{x}$ is

Let $f(x) = x^m$, where $m$ is a non-negative integer. The value of $m$ such that the equality $f^{\prime}(a+b) = f^{\prime}(a) + f^{\prime}(b)$ is valid for all $a, b > 0$ is

If $y=(1+x)(1+x^{2})(1+x^{4}) \ldots (1+x^{2^{n}}),$ then the value of $\left(\frac{d y}{d x}\right)$ at $x=0$ is

$\left\{\frac{d}{d x}\left(\sec x^{\circ}\right)\right\}_{x=30} = $ . . . . . . .

If $y = x + \frac{1}{x}$,then which among the following holds?

If $8 f(x)+6 f\left(\frac{1}{x}\right)=x+5$ and $y=x^2 f(x)$,then $\frac{d y}{d x}$ at $x=-1$ is