Calculus
Implicit differentiation
When y is mixed with x — differentiate both sides and solve for dy/dx.
When y is mixed with x in an equation, differentiate both sides treating y as a function of x — then solve for dy/dx.
Walk through
Step 1 of 5
The setup
Given x² + y² = 25, y is tangled with x. Treat y as a function of x and differentiate both sides.
Every time you differentiate a term containing y, a factor of dy/dx pops out (chain rule). Then just collect all the dy/dx terms on one side and divide.
Your turn
Find dy/dx for x³ + y³ = 6xy.
Watch out
Don't forget the dy/dx factor when differentiating a y term. d/dx(y²) is 2y·dy/dx, not just 2y.
Try it
x² + y² = 25, find dy/dx
2x + 2y · dy/dx = 0. So dy/dx = −x/y.