To find: use part 1 of the fundamental theorem of calculus to find the derivative of the function.
The derivative of the function is
Given information: The function is
Let’s remind of the fundamental theorem of calculus part 1:
The fundamental theorem of calculus part 1: If f is continuous on then the function of g defined by
where is continuous on and differentiable on and .
First , we will use the properties of the definite integral to make the integral match the form in the fundamental theorem, so we have, [ where ]
Since the upper limit of integration is not , we apply the chain rule.
Consider the new function
Differentiation with respect to u,
Hence, The derivative of the function is .
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