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I can't answer the seventh question of advanced mathematics. Choose c, my question is like 2. Ask the great god to answer!
Solution:

Order: z=f(x, y), then:

dz=(? f/? x)dx+(? f/? y)dy

Therefore:

dz=-x? 【e^(-x)]dx+f'y d(x? )={2xf'y-x? [e^(-x)]}dx

At this moment:

z=f(x,x? )=x? [e^(-x]

dz=d{x? [e^(-x)]}=2x[e^(-x)]dx-x? [e^(-x)]dx=(2x-x? )[e^(-x)]dx

2xf'y-x? [e^(-x)]=(2x-x? )[e^(-x)]

f'y=e^(-x)

Choose C.

To answer your question:

1, I don't understand it because you don't understand the role of independent variables, intermediate variables and dependent variables in finding partial derivatives;

2、f'x(x,x? ) is f'x(x, y) in y=x? Instead of f(x, x? ) export values, similar to unary functions, such as:

What does f'(2) mean? Please experience it!

To sum up, your understanding of partial derivatives of binary functions is limited to formulas, but you don't understand them in essence!