Basics of Differentiation

Understand Differentiation as the process of finding the derivative, or rate of change, of a function.
Familiarise with the term derivative and its notations - ‘f’(x) or df(x)/dx.
Be aware that the derivative of a constant is zero and the derivative of a linear term is its coefficient.

Key Rules

Memorise the Power Rule: The derivative of x^n is n*x^(n-1).
Comprehend Chain Rule for finding the derivative of a composite function, denoted as d/dx[ f(g(x)) ].
Grasp the Product Rule applicable to the derivative of a product of two or more functions.
Get a handle on the Quotient Rule for finding the derivatives of quotients of functions.

Appreciate that differentiation is used to solve real-life problems including optimisation and rates of change.
Know that differentiation from first principles is based on the idea of limits and is a proof for differentiating standard functions.
Understand how to find the equation of the tangent to a curve at a given point using differentiation.
Be able to use differentiation to determine turning points on the curve, identifying local maxima, minima, and points of inflection.

Understand how to differentiate exponential functions and log functions.
Recognise that the chain rule can be used to calculate the derivative of functions involving trigonometry and inverse functions.
Be capable of differentiating parametric equations using parametric differentiation.

Regularly tackle past papers, as the process makes a significant contribution to understanding and retention.
Expose yourself to a wide array of questions - straightforward, complex, abstract.
Occasionally study and solve problems in groups for a higher chance of understanding challenging concepts.
Remain persistent and patient when tackling complex differentiation problems.