Question

Найти производную функции: f(x)=((x-3)^3)*(x-1) f(x)=((x^2)-9)*(x+1)

Answer 1

f(x)=(x-3)³ (x-1)

f'(x)=((x-3)³)' (x-1) + (x-1)' (x-3)³ = 3(x-3)²(x-1)+ 1*(x-3)³=(x-3)²(3(x-1)+ (x-3))=

=(x-3)²(3x-3+ x-3)= (x-3)²(4x-6)= 2(2x-3)(x-3)²

f(x)=(x²-9) (x+1)

f'(x)=(x²-9)' (x+1)+ (x+1)' (x²-9) = 2x(x+1)+ 1*(x²-9) = 2x²+2x+x²-9 = 3x²+2x-9

Answer 2

$\\f(x)=(x-3)^3(x-1)\\ f'(x)=3(x-3)^2(x-1)+(x-3)^3\\ f'(x)=(x-3)^2(3(x-1)+x-3)\\ f'(x)=(x-3)^2(3x-3+x-3)\\ f'(x)=(x-3)^2(4x-6)\\ f'(x)=2(x-3)^2(2x-3)$

$\\f(x)=(x^2-9)(x+1)\\ f'(x)=2x(x+1)+x^2-9\\ f'(x)=2x^2+2x+x^2-9\\ f'(x)=3x^2+2x-9$