Question

differentiate f(x) = 2x(x^3 +1)

Answer 1

To differentiate f(x) = 2x(x^3 + 1), we can use the product rule. The product rule states that if we have a function h(x) = g(x)*m(x), then the derivative of h(x) is h'(x) = g'(x)*m(x) + g(x)*m'(x).

Applying the product rule to f(x) = 2x(x^3 + 1), we have:

f'(x) = 2*(x^3 + 1) + 2x*(3x^2)
f'(x) = 2x^3 + 2 + 6x^3
f'(x) = 8x^3 + 2

Therefore, the derivative of f(x) = 2x(x^3 + 1) is f'(x) = 8x^3 + 2.