y=2ax and dydx=log 256 at x=1 then a =

The given function is $y = 2^{a x}$

Differentiate both sides with respect to $x$

$\begin{array}{rcl} \frac{d y}{d x} & = & \frac{d}{d x} (2^{a x}) \\ = & 2^{a x} a \log 2 \end{array}$

Given that $\frac{d y}{d x} a t x = 1 i s \log 256 = \log 2^{8} = 8 \log 2$

Hence,

$\begin{array}{rcl} a 2^{a} & = & 8 \\ = & 2 (2^{2}) \end{array}$

Therefore, $a = 2$

$y = 2^{ax} and \frac{dy}{dx} = \log 256 at x = 1 then a =$