Leibniz Integral Rule

$${\partial\over\partial z}\int_{a(z)}^{b(z)} f(x,z)\,dx = \in... ...rtial b\over\partial z} -f(a(z),z){\partial a\over\partial z}.$$

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 11, 1972.