Question

найдите производную функций номер 748(в,г) 750(а,б)

Answer 1

748
в)
$y=sqrt{x}(8x-10);\ y'=left(sqrt{x}right)'cdotleft(8x-10right)+sqrt{x}cdotleft(8x-10right)'=\ =frac{1}{2sqrt{x}}(8x-10)+sqrt{x}cdot8=4sqrt{x}-frac{5}{sqrt{x}}+8sqrt{x}=\ =12sqrt{x}-frac{5}{sqrt{x}}=frac{12x-5}{sqrt x}$
г)
$y=sqrt{x}(x^4+2);\ y'=left(sqrt{x}right)'cdotleft(x^4+2right)+sqrt{x}cdotleft(x^4+2right)'=\ =frac{1}{2sqrt{x}}(x^4+2)+sqrt{x}cdot4cdot x^3=frac{x^3sqrt{x}}{2}+frac{1}{sqrt{x}}+4x^3sqrt{x}=\ =4frac12x^3sqrt{x}+frac{1}{sqrt{x}}=frac{9x^4+2}{2sqrt{x}}$

750

а)

$y=left(frac1x+1right)left(2x-3right);\ y'=left(frac1x+1right)'cdotleft(2x-3right)+left(frac1x+1right)cdotleft(2x-3right)'=\ =-frac1{x^2}cdotleft(2x-3right)+left(frac1x+1right)cdot2=\ =-frac2x+frac3{x^2}+frac2x+2=2+frac{3}{x^2}$

б)

$y=left(6-frac1xright)left(6x+1right);\ y'=left(6-frac1xright)'cdotleft(6x+1right)+left(6-frac1xright)cdotleft(6x+1right)'=\ =frac1{x^2}cdotleft(6x+1right)+left(6-frac1xright)cdot6=\ =frac6x+frac1{x^2}+36-frac6x=frac{1}{x^2}+36$

Answer 2

а еще

Answer 3

всё