设f(u,v)具有连续二阶偏导,Z=f(e^xsiny,x-2y),求δ^2z⼀δxδy

2024-11-28 12:30:05
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回答1:

z = f(e^xsiny,x-2y)
∂z/∂x = e^xsinyf'<1> + f'<2>
∂^z/∂x∂y = e^xcosyf'<1> + e^xsiny[e^xcosyf''<11>-2f''<12>]
+ [e^xcosyf''<21>-2f''<22>]
= e^xcosyf'<1>+ (1/2)e^(2x)sin2yf''<11>+e^x[cosy-2siny)f''<12> - 2f''<22>