Question

If we ignore air resistance, then the range R(𝜃) of a baseball hit at an angle 𝜃 with respect to the x axis and with initial velocity v0 is given by

R(𝜃) = 1/g(v0)2 sin (2𝜃) for 0 ≤ 𝜃 < 𝜋/2


where g is the acceleration due to gravity.

(a) If v0 = 80 (meters per second) and g = 9.8 (meters per second per second), then

R ' (𝜋/4)

Answer 1

a little more ligibly,
R = v^2/g sin2θ

when you say R', derivative with respect to what?
Hmmm. it appears you mean dR/dθ, with v constant.
dR/dθ = 4v^2/g cos2θ = 4*6400/9.81 * 1/√2 = 1845.25 m/rad