Let u = u (x) and v = v (x) be differentiable to x.

y=uv=u(x)v(x)

According to the definition of derivative, if there is a change of t at x, then the change of y.

Y=u(x+t)v(x+t)-u(x)v(x)

= u(x+t)v(x+t)-u(x)v(x+t)+u(x)v(x+t)-u(x)v(x)

=[u(x+t)-u(x)]* v(t+x)+u(x)*[v(x+t)-v(x)]

y/t = v(x+t)*[u(x+t)-u(x)]/t+u(x)*[v(x+t)-v(x)]t

When t approaches zero, the limit of v(t+x) is v(x).

The limit of u (x+t)-u (x)]/t is u'(x),

The limit of [v (x+t)-v (x)]/t is v'(x),

So there is (uv)' =u'v+uv'

Introduction to calculus:

Calculus, a mathematical concept, is a branch of higher mathematics that studies the differential and integral of functions and related concepts and applications. It is a basic subject of mathematics, including limit, differential calculus, integral calculus and its application.

Differential calculus, including the calculation of derivatives, is a set of theories about the rate of change. It makes the function, velocity, acceleration and curve slope can be discussed with a set of universal symbols. Integral calculus, including the calculation of integral, provides a set of general methods for defining and calculating area and volume.