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Leibniz Rule

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The Leibniz Rule tells us how we can move a differential across an integral sign.

\frac{\partial}{\partial z} \int_{a(z)}^{b(z)} f(x,z)\, dx = \int_{a(z)}^{b(z)} \frac{\partial f}{\partial z}\, dx + f(b(z),z)\frac{\partial b}{\partial z} - f(a(z),z)\frac{\partial a}{\partial z}

Last modified on 22 Jan, 2009