Answer
$r'(t)=\dfrac{(\ln10)10^{2\sqrt{t}}}{\sqrt{t}}$
Work Step by Step
$r(t)=10^{2\sqrt{t}}$
Differentiate using the chain rule:
$r'(t)=(10^{2\sqrt{t}})(\ln10)(2\sqrt{t})'$
Rewriting $2\sqrt{t}$ as $2t^{1/2}$, we proceed with the differentiation process:
$r'(t)=(10^{2\sqrt{t}})(\ln10)(2\sqrt{t})'=(10^{2\sqrt{t}})(\ln10)(2t^{1/2})'=...$
$...=(10^{2\sqrt{t}})(\ln10)(2\dfrac{1}{2}t^{-1/2})=(10^{2\sqrt{t}})(\ln10)(t^{-1/2})$
Simplifying:
$r'(t)=\dfrac{(\ln10)10^{2\sqrt{t}}}{\sqrt{t}}$
