Решите номера.Найдите производную функции.

Решите задачу:

$f(x)=tgx+4\; \; \; x_0=- \pi /4\\f`(x)=(tgx+4)= \frac{1}{cos^2x}\\f`(x_0)=f`(- \pi /4)= \frac{1}{cos^2(- \pi /4)}= \frac{1}{( \sqrt{2}/2)^2 }= \frac{1}{1/2}=2\\\\f(x)= \frac{x+1}{x-1}\; \; \; x_0=2\\f`(x)= \frac{(x+1)`(x-1)-(x+1)(x-1)`}{(x-1)^2}= \frac{x-1-x-1}{(x-1)^2}= -\frac{2}{(x-1)^2}\\f`(x_0)=f`(2)= \frac{-2}{(-2-1)^2}= -\frac{2}{9} \\\\f(x)=x^3+2x\; \; \; x_0=2\\f`(x)=(x^3+2x)`=3x^2+2\\f`(x_0)=f`(2)=3*2^2+2=3*9+2=27+2=29$