Differential calculus

University 5 questions

What differential calculus means

You learn how to find the rate at which a function changes. This helps you work out slopes, analyse graphs, and handle later topics in calculus and applied mathematics.

What you will practise

Differentiate polynomial terms using the power rule
Find the derivative of constant terms
Evaluate a derivative at a given x-value
Read simple function notation such as f(x) and f prime of x

Before you start

You should be comfortable with indices, algebraic terms, and basic function notation. It also helps to know how to substitute values into expressions.

Worked example

One question from this skill's own question bank, shown with its full working.

Question

What is the derivative of x cubed?

x squared
3x squared
3x cubed
x cubed over 3

Answer: 3x squared

Working: Power rule: the derivative of x to the n is n times x to the (n minus 1).

Common mistakes to avoid

Changing the power but forgetting to multiply by the original index
Leaving constants unchanged instead of writing their derivative as zero
Stopping after finding f prime of x and not substituting the given x-value
Dropping negative signs or coefficients when differentiating terms

Curriculum and exam alignment

Tertiary foundation coursework

In Ghanaian university and tertiary foundation study, this usually appears early in calculus before more advanced applications. It supports later tertiary coursework and professional entrance tests that expect you to handle basic rates of change confidently.

Curriculum notes are a general guide to where this work normally sits. Always check the syllabus your school or examination body is currently using.