What does dy/dx mean?

It means 'the rate of change of y with respect to x' — the gradient of the curve.

Why does the constant disappear?

A constant term only moves the whole curve up or down; it doesn't change how steep it is, so its gradient contribution is 0.

Topic guide · SS 3

Calculus

Differentiation made simple: the power rule, differentiating polynomials and finding the gradient of a curve at a point, with WASSCE-style practice.

Start the Differentiation from First Principles lesson →

Calculus explained

Calculus is the maths of change. Differentiation finds the gradient (steepness) of a curve at any point — for a straight line the gradient never changes, but for a curve like y = x² it does.

At WASSCE level you mostly need the power rule, applied to each term of a polynomial, and then substitute a value of x to find the gradient at a point.

Key ideas to remember

Power rule: if y = axⁿ, then dy/dx = naxⁿ⁻¹ — bring the power down and reduce it by 1.
The derivative of a constant is 0; the derivative of ax is a.
Differentiate a polynomial one term at a time.
To find the gradient at a point, substitute its x-value into dy/dx.

Worked example

If y = 3x³ − 9x + 5, find dy/dx.

Step 1: Differentiate each term
3x³ → 9x²
−9x → −9
5 → 0
Step 2: Answer
dy/dx = 9x² − 9

Final answer: 9x² − 9

Practice questions

Have a go, then open the answer to check your working. Every answer was checked by the MathPlug maths engine.

Question 1
Find the gradient of the curve y = 5x⁴ − 9x + 1 at the point where x = 1.
- A−4
- B11
- C12
- D−3
Show answer and working
1. Step 1: Differentiate
  dy/dx = 20x³ − 9
  Why? Multiply by the power, then reduce the power by 1. The constant 1 disappears.
2. Step 2: Substitute x = 1
  dy/dx = 20 × 1³ − 9 = 11
Final answer: 11
Question 2
If y = 4x³ + 2x − 5, find dy/dx.
- A12x³ + 2
- B12x² + 2 − 5
- C12x² + 2
- D4x² + 2
Show answer and working
1. Step 1: Differentiate each term
  4x³ → 12x²
  2x → 2
  −5 → 0
2. Step 2: Answer
  dy/dx = 12x² + 2
Final answer: 12x² + 2
Question 3
Find the gradient of the curve y = 2x⁴ − x + 6 at the point where x = 3.
- A215
- B53
- C165
- D647
Show answer and working
1. Step 1: Differentiate
  dy/dx = 8x³ − 1
  Why? Multiply by the power, then reduce the power by 1. The constant 6 disappears.
2. Step 2: Substitute x = 3
  dy/dx = 8 × 3³ − 1 = 215
Final answer: 215

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Frequently asked questions

What does dy/dx mean?: It means 'the rate of change of y with respect to x' — the gradient of the curve.
Why does the constant disappear?: A constant term only moves the whole curve up or down; it doesn't change how steep it is, so its gradient contribution is 0.