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

The answer to (\partial)/(\partial x)(2x^2y+9xy^3) is 4yx+9y^3

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

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

4 y x + 9 y^{3}

Solution steps

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

\frac{\partial}{\partial x} (2 x^{2} y) = 4 y x

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

= 4 y x + 9 y^{3}

\frac{d}{d t} (sin (t) + cos (t))

\frac{d y}{d x} + 3 y = 5

\frac{\partial}{\partial x} (\frac{1}{y - 3 x})

y = x^{3}, (- 1, 2)

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

What is (\partial)/(\partial x)(2x^2y+9xy^3) ?
The answer to (\partial)/(\partial x)(2x^2y+9xy^3) is 4yx+9y^3