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

The given function is $y=2^{ax}$

Differentiate both sides with respect to $x$

$\begin{array}{rcl}\frac{dy}{dx}& =& \frac{d}{dx}\left(2^{ax}\right)\\ & =& 2^{ax}a\log 2\end{array}$

Given that  $\frac{dy}{dx}at x=1 is \log 256=\log 2^8=8\log 2$

Hence, 

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

Therefore, $a=\boxed{\mathbf{2}}$