Product rule
With the product rule you can calculate the derivative of a product of two functions
Explanation
We start with the function
Substitution in the definition of the derivative gives
 = lim₀ {[f(x + ∆x) ⋅ g(x + ∆x) − f(x) ∕ g(x)] ∕ ∆x}.gif){kind=small}
In the fraction we add f (x + Δx) · g (x) and subtract this also
The limit of a sum is the sum of the limits, so
For Δx→0, these two fractions give the derivatives f ′(x) and g ′(x). As the function f (x) is differentiable, holds f (x + Δx) → f (x), thus
so