Задача 24309 16 - 19 задания Найти производную ...
Условие
математика ВУЗ
1247
Решение
★
y`=((x^2*tgx)*lnx-(x^2*tgx)*lnx)/(ln^2x) =
= (2x*tgx*lnx+(x^2/cos^2x)*lnx - x*tgx)/ln^2x.
17.
y`=(1/(1+(x^3+sqrt(x))^2)*(x^3+sqrt(x))`=
=(3x^2+(1/2sqrt(x)))/(1+(x^2+sqrt(x))^2).
18.
y`=(-1/(1+((tg(x/2)+1)/2))^2)*((tg(x/2)+1)/2)`=
=(-1/(1+((tg(x/2)+1)/2))^2)*(1/2)*(1/(cos^2(x/2)) * (x/2)`=
=-1/(4*(1+((tg(x/2)+1)/2))^2)*(1/(cos^2(x/2)) ).
19.
y`_(x)=y`_(t)/x`_(t)
y`_(t)=(1/sqrt(1-(sqrt(1-t^2))^2)*(sqrt(1-t^2))`=
=(1/sqrt(1-(sqrt(1-t^2))^2)*(-2t/(2sqrt(1-t^2)))=
=-t/(sqrt(t^2))*sqrt(1-t^2))
x`_(t)=(1/(1/sqrt(1-t^2)))*(1/sqrt(1-t^2))`=
=(sqrt(1-t^2))*(-1/2)*(1/sqrt((1-t^2)^3))* (1-t^2)=
=(t/2)/sqrt(1-t^2).
y`=-2/|t|