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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.

Difficulty level: Moderate task
Routine calculation training
Cs translation
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