Найти значения производной функции [tex] y=f(x)[/tex] в заданных точках:
1.)[tex]f(x)=x*tgx; x= \pi ;[/tex]
2.)[tex]f(x)= \frac{x}{x+1}; x=2;[/tex]
3.)[tex]f(x)= \frac{x-1}{x}; x=-2;[/tex]
1.)[tex]f(x)=x*tgx; x= \pi ;[/tex]
2.)[tex]f(x)= \frac{x}{x+1}; x=2;[/tex]
3.)[tex]f(x)= \frac{x-1}{x}; x=-2;[/tex]
More Questions From This User See All
Answers & Comments
Verified answer
1) f`(x)=(x)`·tgx+x·(tgx)`=1·tgx+(x/cos²x)f`(π)=tgπ+(π/cos²π)=0+π/(-1)²=π
2) f`(x)=((x)`·(x+1)-x·(x+1)`)/(x+1)²=(x+1-x)/(x+1)²=1/(x+1)²
f`(2)=1/(2+1)²=1/9
3)f`(x)=((x-1)`·x-(x-1)·(x)`)/(x)²=(x-x+1)/(x)²=1/(x)²
f`(-2)=1/(-2)²=1/4