## calculus

Asking good questions is an important part of doing maths. But what makes a good question?

*x*

^{k}? If you're up to speed with your calculus, you can probably rattle the answer off by heart. But can you prove it?

**Chris Sangwin**introduces an ingenious method for deriving the integral from first principles.

*x*

^{k}really the best one?

**Chris Sangwin**makes an interesting case that it is not.

**Phil Wilson**continues our series on the life and work of Leonhard Euler, who would have turned 300 this year. This article looks at the calculus of variations and a mysterious law of nature that has caused some scientists to reach out for god.

**Lewis Dartnell**explained how chaos on the brain is not only unavoidable but also beneficial. Now he tells us why the same is true for our solar system and sends us on a journey that has been travelled by comets and spacecraft.

**Calculus**is a collection of tools, such as differentiation and integration, for solving problems in mathematics which involve "rates of change" and "areas". In the second of two articles aimed specially at students meeting calculus for the first time, Chris Sangwin tells us how to move on from first principles to differentiation as we know and love it!