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2 ln x^2-ln x?

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May 3, 2018

$y = 2 ln (x^{2}) - ln (x)$ $y=2ln(x^2)-ln(x)$

Remember that $log (a^{b}) = b log (a)$ $log(a^b)=blog(a)$ so $ln (x^{2}) = 2 ln (x)$ $ln(x^2)=2ln(x)$ . Then

$y = 2 (2 ln (x)) - ln (x) = 4 ln (x) - ln (x) = 3 ln (x)$ $y=2(2ln(x))-ln(x)=4ln(x)-ln(x)=3ln(x)$

Remembering that the derivative of $ln (x)$ $ln(x)$ is $1 / x$ $1//x$ , we see that

$\frac{d y}{d x} = \frac{3}{x}$ $dy/dx=3/x$

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