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d 52Example2FunctionR2RConsiderthefunctiongR2Rwithgxx21x22Inthefollowingwecomputethedi erentialDgxforp11TTheGateauxdi erentialforanyx2R2isDgxhd d x1 h12x2 h22

=d 5.2Example2:FunctionR2!RConsiderthefunctiong:R2!Rwithg(x)=x21x22.Inthefollowing wecomputethedi erentialDg(x)forp=(1;1)T:TheG^ateauxdi erentialforanyx2R2isDg(x)(h)=d d (x1+ h1)2(x2+ h2)2

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