I had posted a question earlier which this is related to, but a different equation.(adsbygoogle = window.adsbygoogle || []).push({});

$$\frac{d}{dt} \int_0^t H(t,s)ds = H(t,t) + \int_0^t \frac{\partial H}{\partial t}(t,s)ds$$

This was another formula needed in a proof however I don't see how this one holds either. I tried following a proof of the formula from http://www.math.uconn.edu/~kconrad/blurbs/analysis/diffunderint.pdf (bottom of page 13) but it seemed like it contradicted itself by passing the partial derivative through the integral even though the limits aren't independent of the variable. That and replacing dI/da(t) with dI/da even though a in the second operation is just a constant.

Could someone explain how to get from the LHS of the equation to the right? Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Verifying derivative of multivariable integral equation

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Verifying derivative multivariable |
---|

I How to derive this log related integration formula? |

B When do we use which notation for Delta and Differentiation? |

I Derivative of Euler's formula |

I Partial derivatives in thermodynamics |

I Deriving a function from within an integral with a known solution |

**Physics Forums | Science Articles, Homework Help, Discussion**