Multivariable Calculus · 免费预览

隐函数求导

二元和三元情形下的隐函数定理，用于求隐式定义的曲线与曲面斜率的梯度公式，以及它之所以成立的几何原因。

1. Curves defined without solving

Curves defined without solving

The circle and the folium

The geometric engine is the gradient

When the hypothesis fails

The curve $x^2 y + xy^2 = 6$ passes through $(1, 2)$ . What is the slope of the curve there?

The surface $x^2 + y^2 + z^2 = 14$ passes through $(1, 2, 3)$ . What is its tangent plane there?

On the circle $x^2 + y^2 = 25$ , at which point does the formula $dy/dx = -F_x/F_y$ break down?

For the circle $x^2 + y^2 = 25$ at the point $(3, 4)$ , give the slope of the tangent line as a fraction like -3/4.

For the curve $x^2 y + xy^2 = 6$ at the point $(2, 1)$ , give the slope as a fraction like -3/4.

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