f(x)=7x^3-5x^2+x+1
sa aratam ca f'(x)=(3x-1)(7x-1)

mai explicit daca se poate

f(x) = 7x³-5x²+x+1

f'(x) = 7•3x²-5•2x+1

f'(x) = 21x²-10x+1

f'(x) = 21x²-7x-3x+1

f'(x) = 7x(3x-1)-(3x-1)

f'(x) = (3x-1)(7x-1)

f’(x) = (7x^3-5x^2+x+1)’
f’(x) = (7x^3)’ - (5x^2)’ + x’ + 1’
— (c•f)’ = c • f’ —
f’(x) = 7•(x^3)’ - 5•(x^2)’ + x’ + 1’
— (x^n)’ = n•x^(n-1) —
f’(x) = 7•3•x^2 - 5•2•x + 1 + 0
f’(x) = 21x^2 - 10x + 1
f’(x) = 21x^2 - 3x - 7x + 1
f’(x) = 3x(7x-1) - (7x-1)
f’(x) = (7x-1)(3x-1)