# How do you use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function #h(x) = int sqrt(6 + r^3) dx# from 7 to #x^2#?

We need FTC 1 and the chain rule.

But we can use the chain rule here;

So

Summary

We have

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To find the derivative of the function ( h(x) = \int_{7}^{x^2} \sqrt{6 + r^3} , dr ) using Part 1 of the Fundamental Theorem of Calculus, you need to evaluate the integrand function at the upper limit of integration, which is ( x^2 ), and then multiply by the derivative of the upper limit with respect to ( x ), which is ( 2x ). Therefore, the derivative of the function ( h(x) ) is ( h'(x) = \sqrt{6 + (x^2)^3} \cdot 2x ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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