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

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1
Mar 21, 2018

Application of chain rule.
https://goo.gl/images/TN12uo

$\frac{\mathrm{dy}}{\mathrm{dx}}$=3(lnx)^2 × 1/x

[ First considering $\ln x$ as say p , it becomes $y = {p}^{3}$ , then differentiating it, you'll get $\frac{\mathrm{dy}}{\mathrm{dx}} = 3 {p}^{2}$ as ${p}^{n} = n {p}^{n - 1}$ rule of differentiation,
Then,
Considering $x$ of the $\ln x$ as $p$ you are differentiating $\ln p$ which equals $\left(\frac{1}{p}\right)$, where$\ln$ is nothing but natural logarithm, $\log b a s e \left(e\right) \left(p\right)$
P.S.- I'm considering another variable to clear the idea.]

Hope it helps. :)

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