The derivative identity
![d/(dx)[f(x)g(x)]](/images/equations/ProductRule/Inline1.svg) |  |  |
(1)
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 |  | ![lim_(h->0)[(f(x+h)g(x+h)-f(x+h)g(x))/h+(f(x+h)g(x)-f(x)g(x))/h]](/images/equations/ProductRule/Inline6.svg) |
(2)
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 |  | ![lim_(h->0)[f(x+h)(g(x+h)-g(x))/h+g(x)(f(x+h)-f(x))/h]](/images/equations/ProductRule/Inline9.svg) |
(3)
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 |  |  |
(4)
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where 
denotes the derivative of 
. The Leibniz identity
extends the product rule to higher-order derivatives.
Product Rule
See also
Chain Rule, Derivative, Exponent Laws, Leibniz Identity, Quotient Rule, Related Rates ProblemExplore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 11, 1972.Cite this as:
Weisstein, Eric W. "Product Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProductRule.html