Respuesta
$\frac{d}{dx} \int_{u(x)}^{v(x)} f(t)\,dt = f(v(x)) \cdot v'(x) - f(u(x)) \cdot u'(x)$.
Explicación
Widely tested in JEE Main calculus questions involving limits of the form $\frac{0}{0}$ evaluated using L'Hôpital's Rule.
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What is Leibniz's rule for differentiating an integral with variable limits $\frac{d}{dx} \int_{u(x)}^{v(x)} f(t)\,dt$?
Flashcard de estudio del mazo JEE Main Master Class: Calculus, Mechanics, Coordinate Geometry.