Leibniz Rule

Rarely Tested

Leibniz Rule

For:

$$F(t)=\int_{a(t)}^{b(t)}f(x,t)\,dx$$

$$F'(t)=\int_{a(t)}^{b(t)}\frac{\partial f}{\partial t}\,dx+f(b(t),t)b'(t)-f(a(t),t)a'(t)$$

Usage

- Used to differentiate an integral containing both a parameter and variable limits.

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