Exponential functions involve variables in the exponent. They appear frequently in mathematics, science, and real-world applications, such as compound interest and population growth. The general form is
where \(a\) and \(b\) are constants, and \(e\) is the mathematical constant approximately equal to 2.71828.
To differentiate exponential functions, you usually follow these steps:
- The derivative of \(e^{x}\) is \(e^{x}\) itself.
- For \(e^{u}\), where \(u\) is a function of \(x\), use the chain rule.
This characteristic makes them straightforward to handle in calculus, especially when combined with other rules like the chain rule.