2007-01-15 15:24:38 · 6 answers · asked by dewgongoo 2 in Science & Mathematics ➔ Mathematics
The answer is somewhat complicated.It depends on what the limits of the two integrals are. In the following example, you can say that the derivative of the double integral is just the inner integral. This is a direct result of the Fundamental Theorem of Calculus. See the link I put under "Sources" below.
d z y z
-- ∫ ∫ f(x,y) dx dy = ∫ f(x,z) dx
dz 0 0 0
If the function in the first integral were f(x,y,z) instead of f(x,y), however, the derivative with respect to z is a more complicated expression involving the partial derivative of f(x,y,z) with respect to z.
2007-01-15 18:39:36 · answer #1 · answered by pollux 4 · 0⤊ 0⤋
Derivative Of Double Integral
2016-12-17 15:06:06 · answer #2 · answered by moncayo 4 · 0⤊ 0⤋
Yes, if that you're taking all integrals and derivatives with respect to the same variable.
2007-01-15 15:34:35 · answer #3 · answered by Joni DaNerd 6 · 0⤊ 0⤋
yes
2007-01-15 15:28:15 · answer #4 · answered by Scythian1950 7 · 0⤊ 0⤋
yup its just like eating two donuts then puking the other and you are left with a donut on your stomach hehhe
2007-01-15 15:36:29 · answer #5 · answered by arn_14 2 · 0⤊ 1⤋
yes(:
2007-01-15 15:28:24 · answer #6 · answered by Roxanne 3 · 0⤊ 0⤋