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Derivative of $$$\frac{\ln\left(x\right)}{\ln\left(2\right)}$$$

The calculator will find the derivative of $$$\frac{\ln\left(x\right)}{\ln\left(2\right)}$$$, with steps shown.

Related calculator: Derivative Calculator

Solution

Apply the constant multiple rule $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ with $$$c = \frac{1}{\ln\left(2\right)}$$$ and $$$f{\left(x \right)} = \ln\left(x\right)$$$:

$${\color{red}\left(\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dx} \left(\ln\left(x\right)\right)}{\ln\left(2\right)}\right)}$$

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

$$\frac{{\color{red}\left(\frac{d}{dx} \left(\ln\left(x\right)\right)\right)}}{\ln\left(2\right)} = \frac{{\color{red}\left(\frac{1}{x}\right)}}{\ln\left(2\right)}$$

Thus, $$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right) = \frac{1}{x \ln\left(2\right)}$$$.

Answer

$$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right) = \frac{1}{x \ln\left(2\right)}$$$A