Differentiation

What you'll learn

Differentiating polynomials with the power rule and the chain rule, then using the derivative to find gradients, tangents/normals, rates of change, and stationary points.

• The power rule: bring the power down, then reduce it by one
• A negative or fractional power still obeys the same rule
• The chain rule differentiates a bracket raised to a power: outer power down, times the inner derivative
• The derivative IS the gradient function; substitute an x-value to get the gradient at that point
• A tangent touches the curve with the curve's own gradient; a normal is perpendicular to it
• Connected rates of change chain two derivatives together
• Stationary points are where \(\dfrac{dy}{dx} = 0\); the second derivative (or a sign check) says max or min