Solve \theta (r) = \pi (1 - r/R)

Evaluate

θ (r) = π (1 - \frac{r}{R})

Simplify

More Steps

θ (r) = \frac{π ( R - r )}{R}

Take the derivative of both sides

θ^{'} (r) = \frac{d}{d r} (\frac{π ( R - r )}{R})

Calculate

θ^{'} (r) = \frac{d}{d r} (\frac{π R - π r}{R})

Use differentiation rules

θ^{'} (r) = \frac{1}{R} \times \frac{d}{d r} (π R - π r)

Calculate the derivative

More Steps

θ^{'} (r) = \frac{1}{R} \times (- π)

Solution

θ^{'} (r) = - \frac{π}{R}

\theta (r) = \pi (1 r/r)