高数，高阶导数。

Question

如题所述

Answer 1

u = f(θφ(x) + y^2)
y + e^y = x
d(y + e^y) = dx
dy + e^ydy = dx
dy/dx = y' = 1/(1 + e^y)
y'' = -(y'·e^y)/(1+ e^y)^2 = -e^y/(1+e^y)^3
z = θφ(x) + y^2
z' = θφ'(x) + 2yy'
u' = f '(z)z' = f '(z)(θφ'(x) + 2yy')
u'' = [f '(z)(θφ'(x) + 2yy')]'
= (f '(z))'(θφ'(x) + 2yy') + f '(z)(θφ'(x) + 2yy')'
= (f ''(z)z')(θφ'(x) + 2yy') + f '(z)(θφ''(x) + 2(y')^2 + 2yy'')
将y'和z'代入就得到二阶导数了。