# Implicit Differentiation

• B
For implicit differentiation, is dy/dx of x2+y2 = 50 the same as y2 = 50 - x2 ?

From what I can take it, it'd be a no since.
For x2+y2 = 50,
d/dx (x2+y2) = d/dx (50) --- will eventually be ---> dy/dx = -x/y

Where,
y2 = 50 - x2
y = sqrt(50 - x2)
dy/dx = .5(-x2+50)-.5*(-2x)

mathman
Derivatives (dy/dx) are operators on functions, not on equations. Your post is meaningless.

Mark44
Mentor
For implicit differentiation, is dy/dx of x2+y2 = 50 the same as y2 = 50 - x2 ?
You don't "take dy/dx of" anything. dy/dx is the derivative of y with respect to x. The two equations above are equivalent, meaning that any (x, y) pair that satisifies one equation also satisfies the other equation.

If you differentiate both sides of either equation with respect to x, you should be able to find dy/dx.
From what I can take it, it'd be a no since.
For x2+y2 = 50,
d/dx (x2+y2) = d/dx (50) --- will eventually be ---> dy/dx = -x/y

Where,
y2 = 50 - x2
y = sqrt(50 - x2)
There's no need to solve for y. Just differentiate y2 implicitly with respect to x.
dy/dx = .5(-x2+50)-.5*(-2x)

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