Question

Find the derivative of sin x with respect to x from first principles.

Answer 1

y = sin x as x → x + Δx, y + Δy

∴ (y + Δy) = sin(x + Δx)

Δy = sin(x + Δx) – y

Δy = sin(x + Δx) – sin x ÷ Δx and apply 

lt Δx → 0 on both side