Understanding Polar Coordinates and Derivatives

A square

A straight line

A circle

A flower or clover

Using a slope and an intercept

Using only a y-coordinate

Using only an x-coordinate

Using an angle and a radius

y = θ cos(r)

y = r cos(θ)

y = r sin(θ)

y = θ sin(r)

cos(2θ)

2 cos(2θ)

sin(2θ)

2 sin(2θ)

x = cos(2θ) cos(θ)

x = cos(2θ) sin(θ)

x = sin(2θ) cos(θ)

x = sin(2θ) sin(θ)

Sum rule

Power rule

Product rule

Quotient rule

0

−√2/2

1

√2/2

√2/2

−√2/2

1

0

2

−1

1

0

By multiplying the derivative of y with respect to θ by the derivative of x with respect to θ

By dividing the derivative of y with respect to θ by the derivative of x with respect to θ

By subtracting the derivative of y with respect to θ from the derivative of x with respect to θ

By adding the derivative of y with respect to θ to the derivative of x with respect to θ