Question

Find the first derivative of f(x)=[lnx]^2/x^2

Answer 1

\[ \frac{2}{x^3}-\frac{2 \ln (x^2)}{x^3} \]

Answer 2

i got the same thing too

Answer 3

\[\frac{d}{dx}\frac{[\ln(x)]^2}{x^2}\]

\[=\frac{x^22\ln(x)\frac{1}{x}-\ln(x)^{2}2x}{x^4}\]

\[=\frac{x2\ln(x)-\ln(x)^{2}2x}{x^4}\]

\[=\frac{2\ln(x)-\ln(x)^{2}2}{x^3}\]
\[=\frac{2\ln(x)(1-\ln(x))}{x^3}\]