What is (\partial)/(\partial x)(3x^3-9x+9xy^2) ?

The answer to (\partial)/(\partial x)(3x^3-9x+9xy^2) is 9x^2-9+9y^2

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(\partial)/(\partial x)(3x^3-9x+9xy^2)

\frac{\partial}{\partial x} (3 x^{3} - 9 x + 9 x y^{2})

9 x^{2} - 9 + 9 y^{2}

Solution steps

\frac{\partial}{\partial x} (3 x^{3} - 9 x + 9 x y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (3 x^{3}) - \frac{\partial}{\partial x} (9 x) + \frac{\partial}{\partial x} (9 x y^{2})

\frac{\partial}{\partial x} (3 x^{3}) = 9 x^{2}

\frac{\partial}{\partial x} (9 x) = 9

\frac{\partial}{\partial x} (9 x y^{2}) = 9 y^{2}

= 9 x^{2} - 9 + 9 y^{2}

What is (\partial)/(\partial x)(3x^3-9x+9xy^2) ?
The answer to (\partial)/(\partial x)(3x^3-9x+9xy^2) is 9x^2-9+9y^2