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what is the difference between kramer's rule and chain rule

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Cramer's rule and the chain rule are entirely unrelated.
 
The chain rule is a rule in calculus that lets you take the derivative of a composite function, such as h(x)=g(f(x)). It says that h'(x)=g'(f(x))*f'(x), or "outside derivative times inside derivative".
 
Cramer's rule is a method in linear algebra that allows you to solve a system of linear equations. It can be used to find the inverse of a matrix.