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Step-by-step Solution

Find the derivative of $\ln\left(x\right)^2$

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Answer

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

Step-by-step explanation

Problem to solve:

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

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

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

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

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

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Answer

$\frac{2}{x}\ln\left(x\right)$
$\frac{d}{dx}\left(\ln\left(x\right)^2\right)$

Main topic:

Differential calculus

Used formulas:

2. See formulas

Time to solve it:

~ 0.52 seconds

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