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Parameter Differentiation Under the Integral Sign
For suitable functions:
$$\frac{d}{da}\int_{u(a)}^{v(a)}f(x,a)\,dx=\int_{u(a)}^{v(a)}\frac{\partial f}{\partial a}\,dx+f(v(a),a)v'(a)-f(u(a),a)u'(a)$$
Usage
- Used in advanced parameter-dependent definite integrals.
