# How do you derive an exponential equation?

Table of Contents

- 1 How do you derive an exponential equation?
- 2 What is the derivative of e x What does it mean that the derivative is equal to the value of the function?
- 3 What is the derivative of ex?
- 4 Why is the derivative of E X itself?
- 5 What function has a derivative of E X?
- 6 Why the differentiation of e x is e x?
- 7 How to differentiate E^ (-X) from E^X?
- 8 What does the expression for the derivative mean?

## How do you derive an exponential equation?

The formula for derivative of exponential function is given by, f(x) = ax, f'(x) = ax ln a or d(ax)/dx = ax ln a. f(x) = ex, f'(x) = ex or d(ex)/dx = e.

### What is the derivative of e x What does it mean that the derivative is equal to the value of the function?

Well, whatever value ‘b’ is, we know that it’s also the derivative at x = 0, so we can have some idea of how the rest of the function should look. If we want to estimate f(1) then we can via f(0) + f'(0) * 1, since f(0) = f'(0) our estimate of f(1) is just 2b.

#### What is the derivative of ex?

What does this mean? It means the slope is the same as the function value (the y-value) for all points on the graph. Example: Let’s take the example when x = 2. Since the derivative of ex is ex, then the slope of the tangent line at x = 2 is also e2 ≈ 7.39.

**What is E X derivative?**

It means the slope is the same as the function value (the y-value) for all points on the graph. Example: Let’s take the example when x = 2. Since the derivative of ex is ex, then the slope of the tangent line at x = 2 is also e2 ≈ 7.39.

**Why is derivative of ex itself?**

The derivative of an exponential function is a constant times itself. Using this definition, we see that the function has the following truly remarkable property. Hence is its own derivative. In other words, the slope of the plot of is the same as its height, or the same as its second coordinate.

## Why is the derivative of E X itself?

### What function has a derivative of E X?

Derivative of ex: Proof and Examples. The exponential function is one of the most important functions in calculus. In this page we’ll deduce the expression for the derivative of ex and apply it to calculate the derivative of other exponential functions.

#### Why the differentiation of e x is e x?

Using this formula and substituting the value a = e in f'(x) = ln a ax, we get the differentiation of e to the power x which is given by f'(x) = ln e ex = 1 × ex = ex [Because ln e = 1]. Hence, the derivative of e to the power x is ex.

**What is the derivative of E X?**

The derivative of e x is quite remarkable. The expression for the derivative is the same as the expression that we started with; that is, e x! What does this mean? It means the slope is the same as the function value (the y -value) for all points on the graph. Example: Let’s take the example when x = 2. At this point, the y -value is e 2 ≈ 7.39.

**How do you find the derivative of an exponential function?**

Other Formulas for Derivatives of Exponential Functions . If u is a function of x, we can obtain the derivative of an expression in the form e u: `(d(e^u))/(dx)=e^u(du)/(dx)` If we have an exponential function with some base b, we have the following derivative: `(d(b^u))/(dx)=b^u ln b(du)/(dx)`

## How to differentiate E^ (-X) from E^X?

We can differentiate e^ (-x) using the chain rule. f (x) = e^x and g (x) = -x f (g (x)) = e^ (-x) f (g (x))’ = g’ (x) * f’ (g (x)) = -1 * e^ (-x) = -e^ (-x)

### What does the expression for the derivative mean?

The expression for the derivative is the same as the expression that we started with; that is, e x! What does this mean? It means the slope is the same as the function value (the y -value) for all points on the graph. Example: Let’s take the example when x = 2.