Quick question on typical integration/differentiation. What is the justification for differentiating some integrals with respect to constants in order to obtain results for them, i.e. [itex]\frac{∂}{∂α}[/itex][itex]\int e^{-αx^{2}}dx=\int-x^{2}e^{-αx^{2}}dx[/itex]? It seems to me α is a constant, so it seems a little confusing to even talk about the partial derivative. I guess if you treat the entire integral to be a multivariable function of both x and α, [itex]f(x,α)[/itex] then it's somewhat justified, though I could just as well replace alpha with some number and we'd be stuck with something like [itex]\frac{∂}{∂8}[/itex] which seems very sketchy.(adsbygoogle = window.adsbygoogle || []).push({});

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

Dismiss Notice

Join Physics Forums Today!

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

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

# Differentiating with respect to a constant

Loading...

Similar Threads for Differentiating respect constant |
---|

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

B Product rule OR Partial differentiation |

A Differential operator, inverse thereof |

I Differentiation of sin function where's my mistake? |

I Differentials of order 2 or bigger that are equal to 0 |

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