Exponential Function Derivative Formula

The differentiation formulas that are used to obtain the exponential function’s derivative,

d/dx (ex) = ex

d/dx (ax) = ax · ln a

Exponential Function Formula

Exponential function is defined by the formula f(x) = ax and this is called the exponential function formula. In this article, we have covered the definition of the exponential function, various exponential function formulas, related examples and others in detail.

Table of Content

  • What is Exponential Function?
  • Exponential Growth Formula
  • Exponential Decay Formula
  • Exponential Series
  • Exponential Function Rules
  • Exponential Function Derivative Formula
  • Exponential Function Integration Formula
  • Applications of Exponential Function Formula

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What is Exponential Function?

An exponential function is a mathematical function of the shape f (x) = ax, where ‘x’ is variable and ‘a’ is consistent this is the function’s base and needs to be more than 0....

Exponential Growth Formula

At first, the quantity grows very slowly, then rapidly in Exponential Growth. Over time, the rate of change accelerates. With time, the rate of growth accelerates. The quick expansion is described as an “exponential increase.”...

Exponential Decay Formula

In Exponential Decay, the quantity decreases rapidly at first, then gradually. The rate of change slows over time. The rate of change slows with time. The rapid rise was supposed to create a “exponential decline.”...

Exponential Series

The following power series can be used to define the real exponential function....

Exponential Function Rules

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Exponential Function Derivative Formula

The differentiation formulas that are used to obtain the exponential function’s derivative,...

Exponential Function Integration Formula

The integral of an exponential function is calculated using integration formulae....

Applications of Exponential Function Formula

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Problems on Exponential Function Formula

Problem 1: In 2010, a town had 100,000 inhabitants. How many citizens will there be in ten years if the population grows at an annual rate of 8%?...

FAQs on Exponential Function Formula

What is Exponential Function Formula?...