The derivative of a function of a real variable like 3x³ + 2x measures the sensitivity to change of a quantity.

Derivative Formula:

f'(x) = lim_Δx→0 = (f(x+Δx)–f(x))/Δx

For example,f'(x) = 3x + 10, f'(x) = lim_Δx→0 (f(x+Δx)–f(x))/Δx
=> f'(x) = lim_Δx→0 [3(x+Δx)+10–(3x+10)]/Δx
=> f'(x) = lim_Δx→0 [3x+3Δx+10–3x−10)]/Δx
=> f'(x) = lim_Δx→0 [3Δx]/Δx
=> f'(x) = lim_Δx→0 3
=> f'(x) = 7.