Maths what is e

Its properties have led to it as a "natural" choice as a logarithmic base, and indeed e is also known as the natural base or Naperian base after John Napier. There is the remarkable property that if the function known as the exponential function and also denoted as " " is differentiated with respect to , then the result is the same function. The proof of this can be seen in many textbooks on elementary calculus. This is because some number can always be chosen so that.

Differentiating with respect to gives. When you differentiate , it remains unchanged:. This also means that when you integrate it will remain unchanged apart from the constant of integration. This unique property simplifies many calculations involving. This is really surprising, given that comes from looking at the properties of a circle, and arises from situations which have nothing to do with circles such as compound interest.

Web design by Measured Designs. Hit enter to search or ESC to close. Close Search. Jacob Bernoulli. Love 2 Share Tweet Share. Tags algorithm algorithms cancer careers advisor coding Competition Competition winners cymru data science environment fractions gcse health ks4 machine learning modelling music National 5 pi profile Pythagoras python square root statistics teacher teachers Weather Forecasting whales. Eugene Kidwell 14th October Eugene Kidwell 7th October It appears in many applications.

The exponential function arises whenever a quantity grows or decays at a rate proportional to its current value. Key Terms tangent : A straight line touching a curve at a single point without crossing it.

Learning Objectives Identify some properties and uses of the natural logarithm. Key Takeaways Key Points The natural logarithm is the logarithm with base equal to e.

The number e and the natural logarithm have many applications in calculus, number theory, differential equations, complex numbers, compound interest, and more. Key Terms natural logarithm : The logarithm in base e. Licenses and Attributions.