Computing Derivatives Exercises

Answer

The derivative of e^u is e^u · u'. In this case u = x³ + 2x, so

(e^{x3 + 2x})' = e^{x3 + 2x} · (3x² + 2).

Answer

• The derivative of cos u is -sin u · u'. In this case u = x⁵, therefore (cos (x⁵))' = -sin(x⁵) · (5x⁴)

Answer

• The derivative of u⁵ is 5u⁴ × u'. Since u = cos x, we find ((cos x)⁵)' = 5(cos x)⁴ · (-sin x)

Answer

The derivative of e^u is e^u · u'. Here u = sin x therefore  (e^{sin x})' = e^{sin x} · cos x

Answer

• The derivative of u⁵ is 5u⁴ · u'. Here u = 5x + 6 therefore

((5x + 6)⁵)' = 5(5x + 6)⁴ · (5)

Answer

• The derivative of ln u is . Here u = x² + x therefore