Compute the derivative of the function F(t) F ( t ) = &#x222C;<!-- ∬ -->

Emmy Dillon

Emmy Dillon

Answered question

2022-06-08

Compute the derivative of the function F(t)
F ( t ) = e t x y d x d y
where 0.1 x t
and 0.1 y t
Please help me to find F'(t)
I tried the antiderivatives. But F(t) doesn't seem to be an elementary integral.

Answer & Explanation

stigliy0

stigliy0

Beginner2022-06-09Added 21 answers

Explanation:
0.1 t e x t y d x = y t ( e t 2 y e 0.1 t y )
y t e t 2 y d y and y t e 0.1 t y d y are nonelementary integrals.
MAPLE gave the following result.
1 200 t 2 ( 300 E i 1 ( 10 t 2 ) t 4 + ( 30 t 2 + 1 ) e 10 t 2 + ( 300 t 4 + t 2 ) E i 1 ( t ) E i 1 ( 1 10 ) t 2 110 t 2 e 1 10 + 300 e t ( t 3 + 1 3 t 2 + 1 300 t 1 300 ) )

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