# Chapter 5 - Section 5.4 - The Fundamental Theorem of Calculus - Exercises - Page 323: 93

$\dfrac{d}{d x} \int_a^{u(x)}f(t) dt =f((u(x)) \cdot u'(x)$

#### Work Step by Step

Here, we have $\dfrac{d}{d x}\int_a^{u(x)}f(t) dt= [\dfrac{d}{d(u(x))}\int_a^{u(x)}f(t) dt](\dfrac{d(u(x))}{d x})$ This implies that $\dfrac{d}{d x} \int_a^{u(x)}f(t) dt =f((u(x)) \cdot u'(x)$ The answer can be checked in a CAS (e.g. Maple).

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