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The total differential for composite function
Task number: 3201
Consider the function H:R2→R with the form H(r,α)=xex+y, where x=rcosα and y=rsinα.
Variant 1
Evaluate ∂H∂r and ∂H∂α, ideally with the help of the chain rule.
Variant 2
Determine the total differential of H.
Variant 3
For small ε estimate H(1+ε,ε) with the help of the total differential.