Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
$g (x) = \int_{6}^{x} t^{5} \sin (t) d t$

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$x^{5} \sin (x)$ is the final answer.

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Step 1 ：Given the function $g (x) = \int_{6}^{x} t^{5} \sin (t) d t$ , we are asked to find its derivative.

Step 2 ：According to the Fundamental Theorem of Calculus Part I, the derivative of a function defined by an integral from a to x of f(t) dt is simply f(x).

Step 3 ：Therefore, the derivative of the given function is simply the integrand evaluated at x, which is $x^{5} \sin (x)$ .

Step 4 ： $x^{5} \sin (x)$ is the final answer.

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.g(x)=∫6xt5sin⁡(t)dt

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Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
$g (x) = \int_{6}^{x} t^{5} \sin (t) d t$