y=x+e^(-xy),当x=0时,求y的二次导(d^2y/dx^2)值。
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y=x+e^(-xy),当x=0时,求y的二次导(d^2y/dx^2)值。
y = x + e^(-xy)
When x = 0,y = 0 + e^(-0×y) = 1
dy/dx = 1 + [e^(-xy)]×[-y - xdy/dx] [*]
When x = 0,
dy/dx = 1 + [e^(-0×1]×[-1 - 0×dy/dx] = 1 - 1 = 0
From [*]
d²y/dx² = [e^(-xy]×[-y - xdy/dx]² + [e^(-xy]×[-2dy/dx - xd²y/dx²]
When x = 0
d²y/dx² = 1×[-1 - 0×0]² + 1× [-2×0 - 0×d²y/dx²]
d²y/dx² = 1
When x = 0,y = 0 + e^(-0×y) = 1
dy/dx = 1 + [e^(-xy)]×[-y - xdy/dx] [*]
When x = 0,
dy/dx = 1 + [e^(-0×1]×[-1 - 0×dy/dx] = 1 - 1 = 0
From [*]
d²y/dx² = [e^(-xy]×[-y - xdy/dx]² + [e^(-xy]×[-2dy/dx - xd²y/dx²]
When x = 0
d²y/dx² = 1×[-1 - 0×0]² + 1× [-2×0 - 0×d²y/dx²]
d²y/dx² = 1
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