Prerequisite concepts Differential Calculus Single variable chain rule If $f=f(y)$ and $y=y(x), then \frac{df}{dy}=\frac{df}{dx}\frac{dx}{dy}.$ New prereq concept Chain Rule New taught by A partial derivative can be expressed in terms of other partial derivatives FIXME Representations used No activity! NEEDS NAME $\left(\frac{\partial f}{\partial x}\right)_y$ ENTER LONG DESCRIPTION No activity! NEEDS NAME $\frac{\partial f}{\partial x}$ ENTER LONG DESCRIPTION No activity! NEEDS NAME Chain Rule Diagrams ENTER LONG DESCRIPTION New representation Chain Rule Measurements There is a partial derivative in every direction at any point Directional Derivatives All partial derivatives can be found as a slope of a tangent plane The components of the gradient are partial derivatives Chain Rules There might be experimental limits on which quantities you can measure Differentials allow the finding of partial derivatives when a variable cannot be solved for You can flip a partial derivative if the same variable(s) are constant New needed for concept