What is (\partial)/(\partial x)(x^4y^4+8x^9y) ?

The answer to (\partial)/(\partial x)(x^4y^4+8x^9y) is 4y^4x^3+72yx^8

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(\partial)/(\partial x)(x^4y^4+8x^9y)

\frac{\partial}{\partial x} (x^{4} y^{4} + 8 x^{9} y)

4 y^{4} x^{3} + 72 y x^{8}

Solution steps

\frac{\partial}{\partial x} (x^{4} y^{4} + 8 x^{9} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{4} y^{4}) + \frac{\partial}{\partial x} (8 x^{9} y)

\frac{\partial}{\partial x} (x^{4} y^{4}) = 4 y^{4} x^{3}

\frac{\partial}{\partial x} (8 x^{9} y) = 72 y x^{8}

= 4 y^{4} x^{3} + 72 y x^{8}

What is (\partial)/(\partial x)(x^4y^4+8x^9y) ?
The answer to (\partial)/(\partial x)(x^4y^4+8x^9y) is 4y^4x^3+72yx^8