Question

(x-1)^2/Ln*x знайти похідну

Answer 1

$( \frac{(x - 1) {}^{2} }{ ln(x) } )' = \frac{((x - 1) {}^{2} )' ln(x) - (x - 1) {}^{2}( ln(x) )' }{ln {}^{2} (x)} = \frac{2(x - 1) ln(x) - \frac{1}{x} (x - 1) {}^{2} }{ ln {}^{2} (x) } = \frac{2x(x - 1) ln(x) - (x - 1) {}^{2} }{x ln {}^{2} (x) } = \frac{2x(x - 1) ln(x) }{x ln {}^{2} (x) } - \frac{(x - 1) {}^{2} }{x ln {}^{2} (x) } = \frac{2x - 2}{ ln(x) } - \frac{ {x}^{2} - 2x + 1 }{x ln {}^{2} (x) }$