Question

二阶偏导数 第三行,求混合偏导的时候. 中间的一项. e^xy *(1+xy)f

Answer 1

∂(2xf'1+ye^xy·f'2)/∂y

=∂(2xf'1)/∂y+∂(ye^xy·f'2)/∂y

=2x(∂f'1)/∂y+∂(ye^xy)/∂y·f'2+ye^xy(∂f'2)/∂y

=2x(∂f'1)/∂y+(e^xy+ye^xy·x)f'2+ye^xy(∂f'2)/∂y

=2x(∂f'1)/∂y+e^xy·(1+xy)f'2+ye^xy(∂f'2)/∂y

注意[g(x)f(x)] '=g '(x)f(x)+g(x)f '(x),你所说的那项就是相当与g '(x)f(x)这一项