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PDF-Week18-DirectionalDerivativesandtheGradient;theChainRuleHughes-Hallett PDF document

2x54 7y6fx15 2x4fy24 7y5sorf15 2x4i24 7y5jormoresimplyincomponentnotation15 2x424 7y521fxyp x2y2fxyx2y212fx1 2x2y2122xx p x2y2similarlyfyy p x2y2sorfx

2x54 7y6fx=15 2x4fy=24 7y5sorf=15 2x4~i+24 7y5~jormoresimply incomponentnotation =15 2x4;24 7y521.f(x;y)=p x2+y2f(x;y)=(x2+y2)1=2fx=1 2(x2+y2)1=2(2x)=x p x2+y2similarly fy=y p x2+y2sorf=*x

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