advanced calculus chapter 3 applications of partial dierentiation 37 3 applications of partial dierentiation 3 1 stationary points higher derivatives 2 let u r and f u r the partial ...
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...Advanced calculus chapter applications of partial dierentiation stationary points higher derivatives let u r and f the x y are functions so we can nd their deriva tives write fxy to denote fy dierentiated with respect similarly fxx denotes fx fyx fyy respectively second xx xy yx yy for other notation or just also dierentiate get third on example is xyy derivative obtained from dierentiating then notethat in this true all well behaved particular if both continuous an open subset z xcosy cosy xsiny siny xex yn find possible values n given that have e xe ex nxex thus since result orn a b point tangent plane at horizontal parallel has form c some constant sincethetangentplaneat passesthroughthepoint it recall equation now last putting any value than into gives hence straightforward establish converse solutions equations...