Study notes
Differentiation
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.
What this topic covers
- 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
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