What is (\partial)/(\partial x)(x^5y^8+3x^9y) ?

The answer to (\partial)/(\partial x)(x^5y^8+3x^9y) is 5y^8x^4+27yx^8

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(\partial)/(\partial x)(x^5y^8+3x^9y)

\frac{\partial}{\partial x} (x^{5} y^{8} + 3 x^{9} y)

5 y^{8} x^{4} + 27 y x^{8}

Solution steps

\frac{\partial}{\partial x} (x^{5} y^{8} + 3 x^{9} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{5} y^{8}) + \frac{\partial}{\partial x} (3 x^{9} y)

\frac{\partial}{\partial x} (x^{5} y^{8}) = 5 y^{8} x^{4}

\frac{\partial}{\partial x} (3 x^{9} y) = 27 y x^{8}

= 5 y^{8} x^{4} + 27 y x^{8}

What is (\partial)/(\partial x)(x^5y^8+3x^9y) ?
The answer to (\partial)/(\partial x)(x^5y^8+3x^9y) is 5y^8x^4+27yx^8