Question

знайти похідну функції: y=x^3/ln x^2

Answer 1

$y = \frac{x^3}{\ln{x^2}} \\y'=\frac{(x^3)'\ln{x^2}-x^3*(\ln{x^2})'}{\ln^2{x^2}}=\frac{3x^2\ln{x^2}-x^3*\frac{1}{x^2}*(x^2)'}{\ln^2{x^2}}=\frac{3x^2\ln{x^2}-2x^2}{\ln^2{x^2}}=\frac{x^2(3\ln{x^2}-2)}{\ln^2{x^2}}$