How do you find the derivative of $y = {(ln x)}^{3}$ $y=(ln x)^3$ ?

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Answer 1 · 2015-05-16T15:08:08

Simple chain rule use here.

Be $u = ln x$ $u=lnx$ , then we apply chain rule as follows

$\frac{d y}{d u} \cdot \frac{d u}{d x} = \frac{d y}{d x}$ $(dy)/(du)*(du)/(dx)=(dy)/(dx)$

$\frac{d y}{d x} = 3 u^{2} \cdot d u = 3 {(ln x)}^{2} \cdot \frac{1}{x}$ $(dy)/(dx)=3u^2*du=3(lnx)^2*1/x$

$\frac{d y}{d x} = \frac{3 {(ln x)}^{2}}{x}$ $(dy)/(dx)=(3(lnx)^2)/x$

How do you find the derivative of y=(ln x)^3y=(lnx)3y=(ln x)^3?