Question

Tính đạo hàm y= ( x^2+1)(X^3+1)(x^4+1)

Answer 1

Use the product and power rules:

`y = (x^2+1)(x^3+1)(x^4+1)`

The product rule says

`(\mathrm dy)/(\mathrm dx) = (\mathrm d(x^2+1))/(\mathrm dx)(x^3+1)(x^4+1) + (x^2+1)(\mathrm d(x^3+1))/(\mathrm dx)(x^4+1) + (x^2+1)(x^3+1)(\mathrm d(x^4+1))/(\mathrm dx)`

and using the power rule to compute the remaining derivatives gives

`(\mathrm dy)/(\mathrm dx) = \boxed{2x(x^3+1)(x^4+1) + 3x^2(x^2+1)(x^4+1) + 4x^3(x^2+1)(x^3+1)}`