In order to differentiate the exponential function. f (x) = a x, f (x) = ax, we cannot use power rule as we require the exponent to be a fixed number and the base to be a variable. Instead, we're …

Aug 13, 2025 · In this article, we will learn about the derivative of the exponential function, its formula, proof of the formula, and examples in detail. But before learning about the …

Nov 16, 2022 · In this section we derive the formulas for the derivatives of the exponential and logarithm functions.

In this article, we will study the concept of the derivative of the exponential function and its formula, proof, and graph along with some solved examples to understand better. What is …

The following diagram shows the derivatives of exponential functions. Scroll down the page for more examples and solutions on how to use the derivatives of exponential functions.

To differentiate an exponential function, copy the exponential function and multiply it by the derivative of the power. For example, to differentiate f (x)=e2x, take the function of e2x and …

Nov 14, 2025 · So far, we have learned how to differentiate a variety of functions, including trigonometric, inverse, and implicit functions. In this section, we explore derivatives of …

If it helps, think of the formula as the chain rule being applied to natural exponential functions. The derivative of e raised to the power of a function will simply be e raised to the power of the …

Dec 1, 2025 · It is very clear that the sign of the derivative of an exponential depends on the value of b. If 0 <b <1, the value of the derivative of the function (slope of the tangent line) will be …

Formulas and examples of the derivatives of exponential functions, in calculus, are presented. Several examples, with detailed solutions, involving products, sums and quotients of …