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SingaporeAdditional Mathematics

Differentiation and Its Applications

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What does the derivative measure, and how do we differentiate powers and the standard functions?

Interpret the derivative as a gradient and rate of change, and differentiate powers of x and the standard exponential, logarithmic and trigonometric functions
A focused answer to the O-Level A-Maths outcome on basic differentiation. The meaning of the derivative as a gradient, the power rule, and the derivatives of the standard exponential, logarithmic and trigonometric functions.
9 min answer →

How do the product, quotient and chain rules let us differentiate products, quotients and composite functions?

Apply the product, quotient and chain rules, individually and in combination, to differentiate products, quotients and composite functions
A focused answer to the O-Level A-Maths outcome on the differentiation rules. The product, quotient and chain rules, when to use each, and how to combine them for more elaborate functions.
9 min answer →

How does the chain rule connect the rates at which two related quantities change with time?

Use the chain rule to relate connected rates of change, finding one rate from another for two quantities linked by an equation
A focused answer to the O-Level A-Maths outcome on connected rates of change. Using the chain rule to link the rates at which related quantities vary with time, and solving practical rate problems.
9 min answer →

How do we locate the stationary points of a curve and decide whether each is a maximum, a minimum or a point of inflexion?

Find stationary points by setting the first derivative to zero and determine their nature using the first or second derivative test
A focused answer to the O-Level A-Maths outcome on stationary points. Solving the first derivative equal to zero, and classifying each point as a maximum, minimum or inflexion using the first or second derivative test.
9 min answer →

How do we use the derivative to find the equation of a tangent or a normal to a curve at a point?

Use the derivative as the gradient to find the equations of the tangent and the normal to a curve at a given point
A focused answer to the O-Level A-Maths outcome on tangents and normals. Using the derivative for the tangent gradient, the negative reciprocal for the normal, and writing both line equations at a point.
8 min answer →