CAL009 · Calculus · Class 12 + B.Tech
Implicit differentiation
Implicit differentiation differentiates both sides of an equation in x and y, treating y as a function of x, then solves for dy/dx.
dy/dx = −x/yImplicit differentiation
📐 Formula
x² + y² = r² ⇒ 2x + 2y dy/dx = 0 ⇒ dy/dx = −x/y
✏️ Worked example
On x² + y² = 25 at (3, 4): dy/dx = −3/4.
🌍 Where it is used
Curves that are not functions, like circles; related rates.
❓ Quick check
For x² + y² = 1, dy/dx at (0, 1)?
🏋️ Practice
Easydy/dx for xy = 1?
Answer: −y/x
MediumSlope of x² + y² = 25 at (4, −3)?
Answer: 4/3
Challengedy/dx for y² = x?
Answer: 1/(2y)