Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

A rule used to differentiate ___ functions, where one function is 'inside' another. You differentiate the outer function, then multiply by the derivative of the inner function.

A technique used to find dy/dx when y is not explicitly defined as a function of x, requiring you to differentiate both sides of an equation with respect to x, remembering to multiply by ______ whenever differentiating a y-term.

The derivative of an inverse function g(x) = f⁻¹(x) can be found using the formula g'(x) = 1 / f'(g(x)), highlighting that the slopes of inverse functions at corresponding points are ___.

Equations where both x and y are defined in terms of a third variable, often 't' (time), called a ___. The derivative dy/dx is found by (dy/dt) / (dx/dt).

A coordinate system where points are defined by a distance 'r' from the origin and an angle 'θ'. To find dy/dx, you first convert to ___ equations.