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

Sagot :

LammettHash

Use the product and power rules:

[tex]y = (x^2+1)(x^3+1)(x^4+1)[/tex]

The product rule says

[tex]\dfrac{\mathrm dy}{\mathrm dx} = \dfrac{\mathrm d(x^2+1)}{\mathrm dx}(x^3+1)(x^4+1) + (x^2+1)\dfrac{\mathrm d(x^3+1)}{\mathrm dx}(x^4+1) + (x^2+1)(x^3+1)\dfrac{\mathrm d(x^4+1)}{\mathrm dx}[/tex]

and using the power rule to compute the remaining derivatives gives

[tex]\dfrac{\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)}[/tex]

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