Differentiation
Power rule: d/dx (xn) = nxn−1. Sum, constant multiple, polynomial.
Y12 builds the foundation: differentiate any polynomial. Y13 adds product, quotient, chain rules and special functions (ex, ln, sin, cos).
Worked examples
d/dx (3x2 + 4x − 5) = 6x + 4.
d/dx (x5) = 5x4.
From first principles: f'(x) = limh→0 (f(x+h) − f(x))/h.
Frequently asked questions
What does the derivative mean?
Gradient of the curve at a point; instantaneous rate of change.
Stationary points?
Where f'(x) = 0. Then check sign change (or f''(x)) for max/min.