Question

Найти производную функции а)f(x)=2x^2+5x-8^x ,f' ( б)f(x)=2х^2+1 деленная х-3, f'(- в)f(x)=(3x^2+5x-1)^10, f' (

Answer 1

А) $f'=4x+5-8^x*ln8$
$f'(0)=4*0+5-8^0*ln8=5-ln8$

$f'= (\frac{2x^2+1}{x-3)} )'= \frac{4x*(x-3)-1*(2x^2+1)}{(x-3)^2} = \frac{2x^2-12x+1}{(x-3)^2}$
$f'(-1)'= \frac{2*(-1)^2-12*(-1)+1}{(-1-3)^2} = \frac{15}{16}$

$f'= (3x^2+5x-1)^{10} =10*(3x^2+5x-1)^9*(6x+5)$
$f'(0)=10*(3*0+5*0-1)^9*(6*0+5)=-10*5=-55$