Question

Найдите производную функции

Answer 1

v(a)=(3a-5)²(4a²-1)=(9a²-30a+25)(4a²-1)=36a⁴-120a³+100a²-9a²+30a-25

=36a⁴-120a³+9a²+30a-25;

v`(a)=144a³-360a²+18a+30;

$y`(t)=\frac{(t^2-1)`(t^2+1)-(t^2-1)(t^2+1)`}{(t^2+1)^2}=\frac{2t(t^2+1)-2t(t^2-1)}{(t^2+1)^2}=\\\frac{2t^3+2t-2t^3+2t}{(t^2+1)^2}=\frac{4t}{(t^2+1)^2}$

$v(`h)=\frac{3`(h^2-2h+2)-3(h^2-2h+2)`}{(h^2-2h+2)^2}=\frac{-3(2h-2)}{(h^2-2h+2)^2}=\\\frac{6-6h}{(h^2-2h+2)^2}$