Multivariable Calculus · 免费预览

偏导数

把偏导数理解为竖直截线的斜率，了解求导时只让一个变量变化而其余变量保持不变的机制，以及使变化变量一目了然的记号。

1. Differentiate one variable and freeze the rest

Differentiate one variable and freeze the rest

2. The mechanics on a worked example

The mechanics on a worked example

3. A partial derivative is a slope, not the whole story

A partial derivative is a slope, not the whole story

4. Partials of functions of three variables

Partials of functions of three variables

5. Freezing the right variable

Compute $f_x$ and $f_y$ for $f(x, y) = x^2 y^3$ .

6. Evaluating a partial at a point

For $f(x, y) = x^2 y^3$ , what is $f_y(1, 2)$ ?

7. A chain-rule partial

For $f(x, y) = \sin(xy)$ , what is $f_x(\pi, 1)$ ?

8. A three-variable partial

For $f(x, y, z) = x^2 z + yz^2$ , compute $f_z$ and give the term that involves $y$ , in the form like 2*y*z or y*z^2.

9. The slope of a vertical trace

For the surface $z = x^2 + y^2$ , walk from the point $(1, 1)$ in the pure $x$ direction. Give the slope of the surface along that walk, as a plain number.

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