I think implicit differentiation is pretty difficult. I think having two different variables and needing to know what to do with each can be hard sometimes.. I am not a fan of this either.
Problem:
1. Find dy/dx: 4xy - y^4 = 5x
First take the derivative of each side: d/dx(4xy-y^4) = d/dx(5x)
Then, for the left side of the equation I used the sum difference rule and took d/dx(4xy) and d/dx(y^4): d/dx(4xy)=4x*dy/dx + 4y and d/dx(y^4) =4y^3
and d/dx(5x)=5. So, 4x*dy/dx + 4y - 4y^3 = 5. To work on getting dy/dx by itself I subtracted 4y from the left side of the equation and moved it to the right side, I also added 4y^3 on the left to move it over to the right. 4x*dy/dx =5-4y + 4y^3. Then I divided by 4x. So dy/dx=(5-4y+4y^3)/(4x)
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