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Intermediate Topic 31 of 51 Math for Computing

Derivatives

Rate of change of a function.

How it works

f'(x) is the instantaneous rate of change (limit of slope); rules: power, product, quotient and chain rule (critical for backpropagation).

Where it is used

Optimization and physics.

Common pitfall

Forgetting the chain rule's inner derivative.

Where it fits in the course

Derivatives is topic 31 of 51 in Math for Computing, rated Intermediate. It follows Orthogonality and Projections. The next topic is Partial Derivatives and Gradients.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Math for Computing quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Derivatives?
Rate of change of a function. It belongs to Math for Computing and is an intermediate-level topic.
Where do people use Derivatives?
Optimization and physics.
What is the most common mistake with Derivatives?
Forgetting the chain rule's inner derivative.
What should I learn before this topic?
Start with Orthogonality and Projections, the topic just before it in Math for Computing.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Math for Computing quiz.
Is Derivatives hard to learn?
It is an Intermediate topic. Be comfortable with the Beginner topics in this area first, then read the common pitfall carefully, since it is where most mistakes happen.
How long does it take to learn Derivatives?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Derivatives?
Orthogonality and Projections, Partial Derivatives and Gradients, Singular Value Decomposition are closely connected. The full list is in the related topics section of this page.
What should I study after Derivatives?
Continue with Partial Derivatives and Gradients, the next topic in Math for Computing.

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