Derivatives practice

Practice session

What you practise

Level 1: a single power, such as 2x^5. Level 2: a sum of terms. Level 3: fractions and roots too, such as x^-2 and x^(1/2). Level 4: b of the tangent line, mixed with the rest. The explanation and a calculator are on the derivative calculator page.

Example

Find the slope f'(2) of f(x) = 2x^3 − 6x.

1. 2x^3 → 3 · 2 · x^2 = 6x^2
2. -6x → 1 · (-6) · x^0 = -6
3. f'(x) = 6x^2 − 6, so f'(2) = 18

Answer: 18.

What you need to know

What the 2027 exam syllabus says about the derivative, for the part this module practices.

havo · wiskunde B · subdomain D3

Finding the derivative of power functions with rational exponents, and using the sum and difference rules · source syllabus wiskunde B havo 2027 (Examenblad)

• Power rule, also with negative and fractional exponents
• Write fractions and roots as a power first
• Work out the slope at a point

vwo · wiskunde A (D3) and wiskunde B (C1, C2)

In wiskunde B vwo you also use the derivative to set up the equation of a tangent line · sources syllabus wiskunde A vwo 2027 (Examenblad), syllabus wiskunde B vwo 2027 (Examenblad)

Formula sheet

Print-friendly: use Print in your browser.

• Power rule $$f\left(x\right)=a{x}^n\Rightarrow f^{\prime }\left(x\right)=na{x}^{n-1}$$
• Tangent line at x = p $$y=f^{\prime }\left(p\right)x+b$$

Derivative (afgeleide)

The function f'(x) that gives the slope of the graph of f for every x.

Practice with real exam questions on Examenblad.nl (in Dutch). We do not host past exams.

Frequently asked questions

Why does this module ask for a number and not the derivative itself?

A number can be marked exactly. If your f'(x) is right, the slope at the point comes out right too; if it is wrong, the number shows which step went wrong.

Which rules do I practise here?

The power rule and the sum rule, including negative and fractional exponents, and the tangent line at a point. The chain rule, product rule and quotient rule are not in this module yet.