What is (\partial)/(\partial x)(6x^2y+9xy^3) ?

The answer to (\partial)/(\partial x)(6x^2y+9xy^3) is 12yx+9y^3

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(\partial)/(\partial x)(6x^2y+9xy^3)

\frac{\partial}{\partial x} (6 x^{2} y + 9 x y^{3})

12 y x + 9 y^{3}

Solution steps

\frac{\partial}{\partial x} (6 x^{2} y + 9 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x^{2} y) + \frac{\partial}{\partial x} (9 x y^{3})

\frac{\partial}{\partial x} (6 x^{2} y) = 12 y x

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

= 12 y x + 9 y^{3}

\frac{\partial}{\partial x} (- x y (12 - x - y))

\frac{\partial}{\partial t} (ln (x + t^{2}))

\frac{d}{d x} (\frac{7 + 8 x - 4 x}{x})

\int_{3}^{6} 2 π x (- \frac{3}{2} x + 9) d x

\int \frac{484 - x ^{2}}{x} d x

What is (\partial)/(\partial x)(6x^2y+9xy^3) ?
The answer to (\partial)/(\partial x)(6x^2y+9xy^3) is 12yx+9y^3