Question

Find dy/dx by implicit differentiation"

xe^y-10x+3y=0

i really do need help!

Answer 1

implicit differentation means you assume y is a function of x:

Dx(xe^y) -Dx(10x) +Dx(3y) = Dx(0)

Dx(xe^y) use the product rule:
(dx/dx)e^y + (dy/dx)xe^y = e^y + y'xe^y


Dx(10x) = (dx/dx)(10) = 10

Dx(3y) = 3(dy/dx) = 3y'

Dx(0) = (d0/dx)0 = 0

Get all your y' on one side and everything else to the other:

e^y + y'xe^y -10 +3y' = 0
y'xe^y + 3y' = 10 -e^y
y'(xe^y +3) = 10 -e^y
(dy/dx) =y' =(10-e^y) / (xe^y +3)

That should be it :)

Answer 2

omg!! thank you so much!!!

Answer 3

Implicits confused me at first; but they are just like ll the rest :)

Answer 4

im a lil confused, but im gonna keep studying thank you again

Answer 5

gratz