Answer
$2vsec^{2}(4^{v^{2}}) 4^{v^{2}}ln4$
Work Step by Step
Let $L'(v)$ be the derivative of the function $tan(4^{v^{2}})$.
$L'(v)=\frac{d}{dv}tan(4^{v^{2}})$
$=sec^{2}4^{v^{2}}\frac{d}{dv}(4^{v^{2}})$
$=sec^{2}4^{v^{2}} 4^{v^{2}}ln4\frac{d}{dv}{(v^{2}})$
$=2vsec^{2}(4^{v^{2}}) 4^{v^{2}}ln4$
