# Basic differentiation

Contents

Differentiating functions is not an easy task! Make your first steps in this vast and rich world with some of the most basic differentiation rules, including the Power rule. It will surely make you feel more powerful.

See how you score on these 20 practice questions

If you ever tried to find derivatives using their formal definition, you probably know how tedious that may be. Fortunately, we have ways for finding derivatives much quicker, using differentiation rules! Make your first steps in this fascinating world by working with the more basic rules. For example, the derivative of [f(x)+g(x)] is f'(x)+g'(x), and the derivative of k⋅f(x) is k⋅f'(x).

The power rule says that the derivative of xⁿ is n⋅xⁿ⁻¹. It allows us to quickly find the derivative of any polynomial, and it doesn't even stop there! Make introduction with this simple but powerful rule.

Put the power rule to use by differentiating various polynomials.

Learn how the power rule can be used to differentiate some basic rational functions.

Learn how the power rule can be used to differentiate some basic radical functions.

The derivative of sin(x) is cos(x) and the derivative of cos(x) is -sin(x). How convenient! Practice differentiating functions that include sine and cosine.

The derivative of eˣ is eˣ. That's pretty amazing. The derivative of ln(x) is 1/x, which is just as surprising.

Review your understanding of basic differentiation rules and your knowledge of the derivatives of common functions with some challenge problems.