Derivative of Exponential Functions

Introduction to Derivative of Exponential Functions

The derivative of an exponential function with the base 'a' and exponent 'x' is given by the formula y = d/dx (a^x) = a^x * ln(a). In this formula, y represents the derivative, a is the base of the exponential function, and x is the exponent. The ln(a) term represents the natural logarithm of the base a.

Parameter usage:

• a = base of the exponential function
• x = exponent of the exponential function

Output:

• y = derivative of the exponential function

Data validation

The base a must be a positive number. The exponent x can be any real number.

Summary

This formula provides the derivative of an exponential function with respect to its exponent, and it is a fundamental concept in calculus, engineering, and physics.