What is (\partial)/(\partial x)(2xy^7+x^7y^9) ?

The answer to (\partial)/(\partial x)(2xy^7+x^7y^9) is 2y^7+7y^9x^6

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(\partial)/(\partial x)(2xy^7+x^7y^9)

\frac{\partial}{\partial x} (2 x y^{7} + x^{7} y^{9})

2 y^{7} + 7 y^{9} x^{6}

Solution steps

\frac{\partial}{\partial x} (2 x y^{7} + x^{7} y^{9})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x y^{7}) + \frac{\partial}{\partial x} (x^{7} y^{9})

\frac{\partial}{\partial x} (2 x y^{7}) = 2 y^{7}

\frac{\partial}{\partial x} (x^{7} y^{9}) = 7 y^{9} x^{6}

= 2 y^{7} + 7 y^{9} x^{6}

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What is (\partial)/(\partial x)(2xy^7+x^7y^9) ?
The answer to (\partial)/(\partial x)(2xy^7+x^7y^9) is 2y^7+7y^9x^6