Product Rule For Differentiation

Let u and v be differentiable functions of x. Then the product function

y = u(x) v(x) is differentiable.

y′ = u(x) v′(x) + v(x) u′(x)

This rule can be remembered as:

Derivative of the product of two functions = (1^st function) (derivative of 2^nd function) + (2^nd function) (derivative of 1^st function)