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anonymous
 4 years ago
Integral(e^(ab))da= e^(ab)*b^1
Why?
anonymous
 4 years ago
Integral(e^(ab))da= e^(ab)*b^1 Why?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0As, going the other way: if I differentiate the right equation with respect to a, b doesn't dissapear, as it is a constant, then why does a b^1 materialise in the antiderivative?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1i take it thats a partial and not b(a)?

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1\[D_a(exp({ab}))=exp(ab)*(ab)'\] \[D_a(exp({ab}))=exp(ab)(a'b+ab')\] or maybe if bs a constant \[D_a(exp({ab}))=exp(ab)*b\]

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1we need the 1/b to catch it; 1/b * b = 1

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1in other words, if we dont put something there to catch the "b" that flies out we dont get the derivative we are looking for

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1Dx is a way to notate a derivative operation on something.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1Da means take the derivative of this stuff with respect to a

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1go ahead and replace b with your favorite constant thats not 0

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1youll see that if we dont have a 1/2 in the antiderivative that we end up with : exp(2a)*2 which is NOT what we are trying to undo.

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.1so we apply a useful form of 1 into the antiderivative to help us out; since 1* anything doesnt change its value; we need a "2", or a "b" as the case may be, so lets use 2/2 and just pull out the 1/2 for later

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thanks, after writing that out it clicked.
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