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

Find the derivative of ln(x)x^2

Answer

$x^2\ln\left(x\right)=2x\ln\left(x\right)+x$

Step-by-step explanation

Problem

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

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\ln\left(x\right)$ and $g=x^2$

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

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Answer

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

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.29 seconds