Question

Найти производную sinx *cosx+ 2x^2 *lnx -1/X^4

Answer 1

$left( sin x cdot cos x+ 2x^2 cdot ln x -frac{1}{x^4}right)' = \ left( sin x cdot cos xright)'+ left( 2x^2 cdot ln x right)' -left( frac{1}{x^4}right)' = \ ( sin x)'cos x + sin x (cos x)'+ ( 2x^2)' ln x + 2x^2 cdot (ln x) ' -left( frac{1}{x^4}right)' = \ cos^2 x - sin^2 x + 4x ln x + 2x^2 cdot frac1x + frac{4}{x^5} = \ cos^2 x - sin^2 x + 4x ln x + 2x + frac{4}{x^5}.$