Can I get some help with solving an implicit differentiation problem? :
x^4(x+y)=y^2(3x-y)

Question

Can I get some help with solving an implicit differentiation problem? :
x^4(x+y)=y^2(3x-y)

dumbcow · Answer

use product rule and remember to multiply by dy/dx every time you differentiate a "y" term

$$4x^3 (x+y) + x^4(1 + \frac{dy}{dx}) = 2y \frac{dy}{dx}(3x-y) + y^2 (3-\frac{dy}{dx})$$

anonymous · Answer

alright, thank you for your help

dumbcow · Answer

can you solve for dy/dx from here

anonymous · Answer

yes, I can. though can you show me how you used the product rule to turn $$x^4(x+y)$$ into $$4x^3(x+y)+x^4(1+\frac{ dy }{ dx }$$

anonymous · Answer

because I got everything except that (1+...) in the second term

dumbcow · Answer

derivative of (x+y) = 1 + dy/dx

anonymous · Answer

oh, haha thanks xD I forgot about the x

solomonzelman · Answer

yes, dumbcow, tnx for doing user's problem for him/her  -:(

anonymous · Answer

Refer to the attachment from Mathematica 9.