Differential calculus
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.
What is the derivative of x cubed?
- x squared
- 3x squared
- 3x cubed
- x cubed over 3
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
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.
Related skills
Other University Mathematics skills in Maths, at the same point in the course.
Other Maths topics
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Exams that assess differential calculus
University work on this skill feeds directly into these exam papers. Each page lists the Maths topics that appear on it.
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Practise differential calculus
5 questions with a worked answer after every attempt, and a SmartScore that tracks how close you are to mastery.