SEQULE

Calculus I

Calculus I

The Chain Rule

Differentiate the outside, then multiply by the inside's derivative.

Concept

Rates multiply

If y depends on u and u depends on x, the rates compose: dy/dx = dy/du · du/dx.

In practice: treat the inner expression as a single blob, differentiate the outer function of that blob, then multiply by the blob's derivative.

d/dx f(g(x)) = f′(g(x)) · g′(x)