Question

Can anyone help me out on integration? I need to integrate 2x*e^(xy) +x^2*y*(xy) with respect to y.

Answer 1

*Edit: I need to take the derivative with respect to y

Answer 2

of this: \[P = 2x*\exp(xy) + x^2*y*\exp(xy)\]

Answer 3

lol one sec

Answer 4

kk, and thanks for helping

Answer 5

\[[e^{xy}]_y=(xy)_ye^{xy}=xe^{xy}\]

Answer 6

I have the answer (I am using a Paul's online note's example) But with this one he lost me. I guess I am not good at taking derivatives with respect to y with exp in them....?

Answer 7

you treat x like a constant

Answer 8

for example pretend we have
\[P(y)=4e^{2y}+4ye^{xy}\]

Answer 9

hmm, so for the first part I say: 2x(xy')e^(xy) = 2x*x*e^(xy)?

Answer 10

okay

Answer 11

\[P(y)=4e^{2y}+4ye^{2y}\]
\[P'(y)=4(2y)'e^{2y}+4(1e^{2y}+y(2y)'e^{2y})\]
\[P'(y)=4(2)e^{2y}+4(1e^{2y}+y(2)e^{2y})\]

Answer 12

\[P=2xe^{xy}+x^2ye^{xy}\]
\[P_y=2x \cdot (xy)_ye^{xy}+x^2 \cdot[ (y)_ye^{xy}+y(e^{xy})_y]\]

Answer 13

\[P_y=2x(x)e^{xy}+x^2[1e^{xy}+y(xy)_ye^{xy}]\]

Answer 14

\[P_y=2x^2e^{xy}+x^2[e^{xy}+y(x)e^{xy}]\]

Answer 15

\[P_y=2x^2e^{xy}+x^2e^{xy}+x^3ye^{xy}\]

Answer 16

OH! I understand! I was leaving out the derivative of y, and lumped the derivative of y and e^(xy) together. I was wondering why Mr. Paul had another factor to his derivative....Okay! Thanks for your help!

Answer 17

yeah product rule for the win!

Answer 18

I know! XD