Answer
$y'=(\pi\ln10)(\sec^{2}\pi\theta)(10^{\tan\pi\theta})$
Work Step by Step
$y=10^{\tan\pi\theta}$
Start the differentiation process by using the chain rule:
$y'=(10^{\tan\pi\theta})(\ln10)(\tan\pi\theta)'=...$
Use the chain rule again to evaluate the derivative indicated and simplify:
$...=(10^{\tan\pi\theta})(\ln10)(\sec^{2}\pi\theta)(\pi\theta)'=...$
$...=(\pi\ln10)(\sec^{2}\pi\theta)(10^{\tan\pi\theta})$
