Find the derivative.

$\frac{d}{dx}{\displaystyle \underset{1}{\overset{cosx}{}}}13t^{12}dt$

a$.$ by evaluating the integral and differentiating the result.

b$.$ by differentiating the integral directly.

a$.$ Evaluate the definite integral.

$\frac{d}{dx}{\displaystyle \underset{1}{\overset{cosx}{}}}13t^{12}dt=\frac{d}{dx}$

$($Simplify your answer. Use integers or fractions for any numbers in the expression.$)$

Find the derivative of the evaluated integral.

$\frac{d}{dx}{\displaystyle \underset{1}{\overset{cosx}{}}}13t^{12}dt=$

$($Simplify your answer. Use integers or fractions for any numbers in the expression.$)$

b$.$ Which of the following is the correct way to find the derivative of the given integral directly?

A$.$ Use the Fundamental Theorem of Calculus, Part $1,$ with $1$ as lower limit and $cosx$ as upper limit$,$ and then use the product rule of differentiation.

B$.$ Use the Fundamental Theorem of Calculus, Part $1,$ with $cosx$ as lower limit and $1$ as upper limit$,$ and then use the product rule of differentiation.

C$.$ Use the Fundamental Theorem of Calculus, Part $1,$ with $cosx$ as lower limit and $1$ as upper limit$,$ and then use the chain rule of differentiation.

D$.$ Use the Fundamental Theorem of Calculus, Part $1,$ with $1$ as lower limit and $cosx$ as upper limit$,$ and then use the chain rule of differentiation.

Therefore, $\frac{d}{dx}{\displaystyle \underset{1}{\overset{cosx}{}}}13t^{12}dt=$

$($Simplify your answer. Use integers or fractions for any numbers in the expression.$)$