# How do you find the derivative of root4(lnx)?

Jun 16, 2016

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{1}{4 x {\left(\sqrt[4]{\ln} x\right)}^{3}}$

#### Explanation:

We use the chain rule here.

As $f \left(x\right) = {\left(\ln x\right)}^{\frac{1}{4}}$

$\frac{\mathrm{df}}{\mathrm{dx}} = \frac{1}{4} \times {\left(\ln x\right)}^{\frac{1}{4} - 1} \times \frac{1}{x}$

or $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{1}{4} \times {\left(\ln x\right)}^{- \frac{3}{4}} \times \frac{1}{x}$

i.e. $\frac{\mathrm{df}}{\mathrm{dx}} = \frac{1}{4 x {\left(\sqrt[4]{\ln} x\right)}^{3}}$