How do I find the derivative of ln(ln(2x))?

May 11, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{x \ln \left(2 x\right)}$

Explanation:

$y = \ln \left(\ln \left(2 x\right)\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left[\ln \left(\ln \left(2 x\right)\right)\right]$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\frac{d}{\mathrm{dx}} \left[\ln \left(2 x\right)\right]}{\ln} \left(2 x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(\frac{\frac{d}{\mathrm{dx}} \left[2 x\right]}{2 x}\right)}{\ln} \left(2 x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(\frac{2}{2 x}\right)}{\ln} \left(2 x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(\frac{1}{x}\right)}{\ln} \left(2 x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{x \ln \left(2 x\right)}$