Question

Вычислите
F'(-pi/2), если f(x)=x cosx
F'(-1), если f(x)=(3x+4)^5

Answer 1

$1) f(x)=xcosx \ f'(x) = (xcosx)'=(x)'cosx+x(cosx)'=cosx-xsinx \ f'( -pi /2) = cos(-pi/2)-(-pi/2)sin(-pi/2)=0+pi/2*(-1)= - pi/2 \ \ 2) f(x)=(3x+4)^{5} \ f'(x) = 5(3x+4)^{4}*3 = 15(3x+4)^{4} \ f'(-1) = 15(-3+4)^{4} = 15$