Difference between revisions of "Product rule"
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==See also== | ==See also== | ||
* [[Chain rule]] | * [[Chain rule]] | ||
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Latest revision as of 18:45, 28 August 2015
Definition
Given two functions f:R→R and g:R→R which are differentiable (at p) the composite function h:R→R where h=fg has derivative:
- dhdx|p=ddx[fg]|p=f(p)dgdx|p+g(p)dfdx|p
- Phonetically first times derivative of second plus second times derivative of first
Example
- 4x2e−x
- ddx[4x2e−x]=4x2ddx[e−x]+e−xddx[4x2]
- =4x2(−1)e−x+4e−xddx[x2]
- =4e−x(ddx[x2]−x2)
- =4e−x(2x−x2)
- =4xe−x(2−x)
- ddx[4x2e−x]=4x2ddx[e−x]+e−xddx[4x2]