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Derivative of $$$\ln\left(x\right)$$$

The calculator will find the derivative of $$$\ln\left(x\right)$$$, with steps shown.

Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps

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Your Input

Find $$$\frac{d}{dx} \left(\ln\left(x\right)\right)$$$.

Solution

The derivative of the natural logarithm is $$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$:

$${\color{red}\left(\frac{d}{dx} \left(\ln\left(x\right)\right)\right)} = {\color{red}\left(\frac{1}{x}\right)}$$

Thus, $$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$.

Answer

$$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$A

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function