Implicit differentiation of 5x^2-2xy+7^y

Answer 1

Two assumptions
1. you want dy/dx
2. You have the equation 5x^2 - 2xy + 7y^2 = 0

10x - 2x dy/dx - 2y + 14y dy/dx = 0
dy/dx( 14y - 2x) = 2y - 10x
dy/dx = (2y-10x)/(14y - 2x) = (y - 5x)/(7y - x)

Answer 2

No, the equation is
5x^2-2xy+7^y

Last term has 7 to the y power....

Answer 3

Ouch, nasty term ...

the derivative of 7^y would be
(ln7)(7^y)dy/dx

I am sure you can make the necessary changes .

Answer 4

Yes...very nasty! Thanks