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Implicit Differentiation Calculator

Find dy/dx for any implicit equation with full step-by-step working. Supports polynomial, trigonometric, exponential, logarithmic, and mixed terms — plus second derivatives and tangent line equations.

Chain rule · Product rule · Implicit y terms · Second derivative d²y/dx² · Tangent line at a point

Implicit Equation F(x, y) = 0

Enter both sides — calculator differentiates term by term

Left side F(x,y)

Right side G(x,y)

x² + y² = 25

Point x₀ (optional — for tangent line)

Point y₀ (optional — for tangent line)

Quick Examples

Result Preview

dy/dx =

—

Equation type—

Rules used—

Slope at point—

Differentiation Rules

d/dx[xⁿ]nxⁿ⁻¹

d/dx[yⁿ]nyⁿ⁻¹·y'

d/dx[xy]y + xy'

d/dx[sin y]cos(y)·y'

d/dx[cos y]−sin(y)·y'

d/dx[tan y]sec²(y)·y'

d/dx[eʸ]eʸ·y'

d/dx[ln y](1/y)·y'

d/dx[f·g]f'g + fg'

d/dx[f/g](f'g−fg')/g²

The Key Idea

Chain rule on y: Any time you differentiate a function of y with respect to x, you must multiply by dy/dx (written y').

Product rule: For terms like x²y, treat x² and y as separate functions: d/dx[x²y] = 2xy + x²y'

Isolate y': After differentiating both sides, collect all y' terms on one side and factor.

Input Format

Powers: x^2, y^3

Multiply: x*y, 2*x

Trig: sin(x), cos(y), tan(x+y)

Exp/Log: e^y, ln(x), log(y)

Implicit Differentiation Calculator

Implicit Equation F(x, y) = 0

Result

Step-by-Step Solution

Second Derivative d²y/dx²

Tangent & Normal Lines