Implicit Differentiation Calculator

Find dy/dx for implicitly defined curves using implicit differentiation.

Curve Type

a

b

c

r

x value

y value

Point (3, 4) is ON the curve

Implicit Derivative

Equation: x² + y² = 5²

dy/dx =

-x/y

At (3, 4): dy/dx =

-0.75

Step-by-Step Solution

Step 1:

Differentiate both sides: d/dx(x² + y²) = d/dx(r²)

Step 2:

2x + 2y(dy/dx) = 0

Step 3:

2y(dy/dx) = -2x

Step 4:

dy/dx = -x/y

Lines at Point

Tangent:y = -0.75x + 6.25

Normal:y = 1.333333x + 0