Related Rates Problem

A related rates problem is the determination of the rate at which a function defined in terms of other functions changes.

Related rates problems can be solved by computing derivatives for appropriate combinations of functions using rules such as the chain rule

[画像: (dy)/(dx)=(dy)/(du)·(du)/(dx) ]

(1)

(for y=f(g(x)) and u=g(x)),product rule

[画像: d/(dx)[f(x)g(x)]=f(x)(dg)/(dx)+g(x)(df)/(dx), ]

(2)

[画像: d/(dx)[(f(x))/(g(x))]=(g(x)(df)/(dx)-f(x)(dg)/(dx))/([g(x)]^2), ]

(3)

[画像: d/(dx)[f(x)+g(x)]=(df)/(dx)+(dg)/(dx), ]

(4)

[画像: d/(dx)(x^n)=nx^(n-1). ]

(5)

See also

Chain Rule, Derivative, Power Rule, Product Rule, Quotient Rule, Sum Rule

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Cite this as:

Weisstein, Eric W. "Related Rates Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RelatedRatesProblem.html

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