**Related Pages**Natural LogarithmLogarithmic FunctionsDerivative RulesCalculus Lessons

### Natural log in (ln)

The natural Log is the logarithm come the basic e, whereby e is one irrational continuous approximately equal to 2.718281828. The organic logarithm is commonly written ln(x) or loge(x).

You are watching: Derivative of ln(e^x)

The herbal log is the inverse role of the exponential function. Lock are connected by the following identities:eln(x) = xln(ex) = x

### Derivative of ln(x)

Using the Chain Rule, we get

**Example:**Differentiate y = ln(x2 +1)

**Solution:**Using the Chain Rule, us get

**Example:**Differentiate

**Solution:**

### Derivatives of Logarithmic Functions

The derivative of the natural logarithmic role (ln

The following are the formulas for the derivatives the logarithmic functions:

**Examples:**Find the derivatives for the following logarithmic functions:

Find the derivatives because that the adhering to logarithmic functions:

**Examples:**

How to identify the natural logarithmic function?

**Examples:**Determine the derivative that the function.

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How to distinguish the organic logarithmic duty using the chain rule?

**Example:**Determine the derivative that the function.f(x) = 5ln(x3)

We offer two justifications for the formula for the derivative that the natural log function. If you want to watch where this formula come from, this is the video clip to watch.

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