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Often math equations can be simplified by substituting variable expression for a single new variable. This substitution is called change of variables.
Often times change of variables can be straight forward, but not always. Here are some cases to watch out for:
- in differentiation -- don't forget the chain rule
- in integrals -- what would the chain rule do here
- in Probability density functions -- special case of substitution inside integrals with extra conditions on the substitution function