Find an equation of the tangent line to the curve y = 8x sin(x) at the point (π/2, 4π).

Answer 1

In point slope form, the equation is

y - y₁ = m(x - x₁)

x₁ = π/2

y₁ = 4π

Get m by evaluating dy/dx at x₁ = π/2. Use the product rule.

dy/dx = 8 sin(x) + 8x cos(x)

Evaluate at π/2 to get m, and finish from here.