1. Differentiation under the integral sign is not allowed for improper integrals. 2. You can differentiate both sides just by adding an integral sign alone. 3. The main difference is that the integral sign is smaller. 4. We claim that the passage of the limit under the integral sign is valid. 5. I'm interested in the formal justification for differentiating under an integral sign . 6. Then I come along and try differentiating under the integral sign , and often it worked. 7. See Differentiation under the integral sign . 8. But the introduction of the integral sign by Leibniz clearly paved the way for a summation sign. 9. Evaluating a mixture of integrals and derivatives can be done by using theorem differentiation under the integral sign . 10. It shows the spectacular barred spiral galaxy NGC 6872 that is shaped like an " integral sign ".
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