The Chain Rule

The chain rule along paths

Several independent variables

Implicit differentiation revisited

The chain rule's linear algebra

For z = f(x, y) with x = x(t) and y = y(t), the derivative dz/dt equals which expression?

In multivariable chain rule computations, the tree diagram serves what purpose?

For F(x, y) = 0 defining y implicitly, the derivative dy/dx equals which expression?

For z = f(x, y) with x = r cos theta, y = r sin theta, the partial dz/dr equals which expression?

For z = xy on the path x = cos t, y = sin t, the chain rule gives dz/dt equal to which expression?

For z = f(x, y) along a path, the chain rule has one term per intermediate variable. As a number, how many terms? Answer with a number.

The implicit differentiation formula dy/dx = -F_x/F_y carries a minus sign. As a sign, what is it? Answer with the single character.

The matrix of all first partials of a vector-valued change of variables is named for which mathematician, surname only? Answer in lowercase.

For w = f(x, y, z) with each of x, y, z functions of t, the total derivative dw/dt has how many terms?

The path x = cos t, y = sin t keeps x squared + y squared constant. As a number, what is that constant? Answer with a number.