# Calculate the second derivative of the function f(x)=\ln(4x^2-x)

Calculate the second derivative of the function
$f\left(x\right)=\mathrm{ln}\left(4{x}^{2}-x\right)$
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Ostrakodec3
Solution:
$f\left(x\right)=\mathrm{ln}\left(4{x}^{2}-x\right)\phantom{\rule{0ex}{0ex}}{f}^{\prime }\left(x\right)=\frac{1}{4{x}^{2}-x}\left(8x-1\right)\phantom{\rule{0ex}{0ex}}{f}^{\prime }\left(x\right)=\frac{8x-1}{4{x}^{2}-x}\phantom{\rule{0ex}{0ex}}{f}^{″}\left(x\right)=\frac{\left(4{x}^{2}-x\right)\left(8-0\right)-\left(8x-1\right)\left(8x-1\right)}{\left(4{x}^{2}-x{\right)}^{2}}\phantom{\rule{0ex}{0ex}}{f}^{″}\left(x\right)=\frac{8\left(4{x}^{2}-x\right)-\left(8x-1{\right)}^{2}}{\left(4{x}^{2}-x{\right)}^{2}}\phantom{\rule{0ex}{0ex}}{f}^{″}\left(x\right)=\frac{8x-32{x}^{2}-1}{\left(4{x}^{2}-x{\right)}^{2}}$