Differentiation · Grade 12

In Grade 12 you learn: the gradient of a curve.

Differentiation finds the gradient of a curve at any point. This is the rate at which one quantity changes as another changes. The derivative dy/dx is the limit of the gradient of a chord as the chord shrinks to a point. For powers of x it follows a simple rule.

Key facts

• First principles: f′(x) is the limit of (f(x + h) − f(x))/h as h → 0.
• Differentiate term by term. A constant differentiates to 0.