Question

derivative of xe^(xy) HELP!

Answer 1

With respect to what?

Answer 2

im thinking to use product rule but i don't know how to do differentiation of e^(xy)

Answer 3

Is it d/dx or d/dy?

Answer 4

d/dx

Answer 5

actually both

Answer 6

So its two questions or is it multivariable calc?

Answer 7

two questions

Answer 8

it's part of finding an equation of the tangent planes

Answer 9

d(xe^(xy))/dy = x*y*e^(xy)

For d/dx you can use product rule

d/dx=u'v+uv'
let u=x
let v=e^(xy)
u'v = 1*e^(xy)
uv' = x*x*e^(xy)

Answer 10

so it's [ 1*e^(xy) + x*e^(xy)*x ] right?

Answer 11

very last *x was from the d/dx e^(xy) right?

Answer 12

ok i got the fx ! what about fy???

Answer 13

is it just x*e^(xy)*y ?

Answer 14

just like fx?

Answer 15

Yeah

Answer 16

d/dx means anything that isnt x can be treated as if it where a constant.
d/dy means the same with y.
So you can think of doing it d/dx as if y was a 5.
Now that im writing this im realizing i did it wrong.
Should be
d(xe^(xy))/dy = x*x*e^(xy)

d/dx=u'v+uv'
let u=x
let v=e^(xy)
u'v = 1*e^(xy)
uv' = x*y*e^(xy)

Answer 17

so what's d/dy ?

Answer 18

for that i don't need to use product rule right?

Answer 19

No, x is considered a constant. So you can think of it as 5e^(5y).
The derivative of that is easy, just 5*5e^(5y).

Rather than use numbers, its easier to work with if you substitute all constant 'variables' with letters you dont usually derive like a,b,c. Just remember to substitute x back in for your final answer.

Answer 20

so d/dy xe^(xy) is y*e^(xy) ?

Answer 21

You should get x*x*e^(xy)

Answer 22

for d/dy ?

Answer 23

oh

Answer 24

now what i got it.. i misunderstood sorry