Calc2.13

From Exampleproblems

Find the derivative of $f(x)\,$ with respect to $x\,$ : $f(x)=\int_{5}^{x}27t^t\sin (t-1)\,dt\,$

Again, this problem uses the Second Fundamental Theorem of Calculus. Since the function is just an integral from a constant to $x\,$ , all we do to take the derivative with respect to $x\,$ is plug $x\,$ into the inner function, $f(t)\,$ . The fact that the function is so complicated does not change things.

$f'(x)=27x^x\sin (x-1)\,$