## 3.9: Derivatives of Ln, General Exponential & Log Functions

The derivative of both sides with respect to x, do a little bit of implicit differentiation. Really just an application of the chain rule. So, on the left-hand side right over here, this is going to be the

## The derivative of lnx and examples

It’s possible to generalize the derivative of expressions in the form ln (ax) (where a is a constant value): The derivative of ln (ax) = 1/x (Regardless of the value of the constant, the

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## Differentiating logarithmic functions review

Solution: 1.) We are taking the natural logarithm of x 2 + 5, so f (x) = x 2 + 5. Taking the derivative of that gives us f' (x) = 2x. 2.) Now, let’s take f (x), f' (x)

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## Logarithmic Differentiation

Find f ′ (x) by first expanding the function and then differentiating. Step 1 Use the properties of logarithms to expand the function. f(x) = ln( √x x2 + 4) = ln( x1 / 2 x2 + 4) = 1 2lnx − ln(x2 + 4)

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## Derivative of ln x (Natural Log)

f (x) = ln(x) The derivative of f(x) is: f ' (x) = 1 / x. Integral of natural logarithm. The integral of the natural logarithm function is given by: When. f (x) = ln(x) The integral of f(x) is: ∫ f (x)dx = ∫ ln(x)dx = x ∙ (ln(x) - 1) + C. Ln of 0. The natural

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