rule

In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as




(
f
⋅
g

)
′

=

f
′

⋅
g
+
f
⋅

g
′



{\displaystyle (f\cdot g)'=f'\cdot g+f\cdot g'}
or in Leibniz's notation as







d

d
x




(
u
⋅
v
)
=




d
u


d
x




⋅
v
+
u
⋅




d
v


d
x




.


{\displaystyle {\dfrac {d}{dx}}(u\cdot v)={\dfrac {du}{dx}}\cdot v+u\cdot {\dfrac {dv}{dx}}.}
The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts.

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