Question

Find (dy/dx) for ye^xy=3x

Answer 1

this requires implicit differentiation, take the dirivative of each term is your first step

Answer 2

um Ive already tried to do that and that is why i came to this site

Answer 3

ok, for the left side: you have to use rules to take the derivative. do you know which ones?

Answer 4

no

Answer 5

your going to want to start with the product rule to derive y*e^xy

Answer 6

would it be y* ln^xy

Answer 7

have you learned how to take the derivative of 'e'? you dont need to use Ln for this

Answer 8

no I have not

Answer 9

Product rule: f'(x)g(x)+f(x)g'(x)
so f(x) would be y
g(x) would be e^xy
in this situation, whats the derivative of y?

Answer 10

just y

Answer 11

well, your taking the derivative with respect to x, so the derivative of y would be dy/dx.

Answer 12

oh ok

Answer 13

do you remember that from class? I just want to make sure im not confusing you

Answer 14

no you are fine

Answer 15

ok, now do you rember how to find the derivative of e^xy?

Answer 16

ex and ey

Answer 17

you have to use the chain rule for this one, have you used the chain rule beore?

Answer 18

yes

Answer 19

hold on a minute ye^x

Answer 20

great! so use the chain rule to find the derivative of e^xy, remember the derivative of y is dy/dx.

Answer 21

they threw a curve at you, its 'xy' so you need to use a product rule again, inside of the chain rule

Answer 22

ye^x

Answer 23

ok, i worked out the problem. you can check my answer:
dy/dx=(3-y)/(e^xy(1+xy))

Answer 24

ok um I checked it and it looks good

Answer 25

ok, i hoped that helped a little bit

Answer 26

yes it did thanks