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Calculus

University

Calculus (University Level)

Implicit Differentiation (Circle)

Find dy/dx implicitly for the circle equation x² + y² = r² at point (x₀, y₀).

Standard Formula

x² + y² = r² → dy/dx = −x/y

Interactive Sandbox

Live Reactive

Adjust values in real-time and observe mathematical cause-and-effect

Radius of circle(Real number)

120

x-coordinate of point(Real number)

120

Live EquationFormula Proof

x² + y² = 5² → dy/dx = −x/y = -0.75

Tangent Line dy/dx

Calculated Solution

-0.75

Direct computational model evaluating Implicit Differentiation (Circle).

Variable Mechanics

Roles, constraints & impacts

2 Params

Radius of circle

ImpactPrimary formula parameter

ConstraintReal number

x-coordinate of point

ImpactPrimary formula parameter

ConstraintReal number

At a Glance

Gotchas, units & real-world use

Essential

Formula Nature & Mechanics

Direct computational model evaluating Implicit Differentiation (Circle).

Common Mistakes & Traps

Ensure all input measurements share consistent units before calculating.
Check for denominator values approaching zero to prevent undefined division.
Follow standard order of operations (PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract).

Dimensional Analysis & Units

Direct evaluation matching formula variable dimensions.

Real-World & Industry Application

Widely utilized across modern calculus applications, academic analysis, and engineering estimations.

📖 Beginner's guideImplicit Differentiation Explained SimplyLearn implicit differentiation step by step using the circle x² + y² = r², find dy/dx = −x/y, avoid common mistakes, and try a free calculator with steps.

Worked Example: Implicit Differentiation (Circle)

Given:

r = 5
x0 = 3

x²+y²=25 at x=3: y=4
2x+2y(dy/dx)=0 → dy/dx = -x/y = -3/4 = -0.75

Answer: -0.75

Frequently Asked Questions

What is the Implicit Differentiation (Circle) formula?

x² + y² = r² → dy/dx = −x/y. Find dy/dx implicitly for the circle equation x² + y² = r² at point (x₀, y₀).

How do I calculate Implicit Differentiation (Circle)?

Enter Radius of circle (r), x-coordinate of point (x0) into the calculator. It applies x² + y² = r² → dy/dx = −x/y and shows every step of the working.

Related Calculus Calculators

Power Rule for Derivativesd/dx(xⁿ) = n × x^(n-1)Definite Integral (Power Rule)∫[a to b] x^n dx = [x^(n+1)/(n+1)]|[a to b]Partial Derivative∂f/∂x = lim[h→0] (f(x+h,y) - f(x,y))/h Chain Rule (Derivative)d/dx[f(g(x))] = f'(g(x)) · g'(x)Product Rule (Derivative)d/dx[f·g] = f'·g + f·g'Quotient Rule (Derivative)d/dx[f/g] = (f'·g − f·g') / g²

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