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

The answer to (\partial)/(\partial x)(x^9y^9-x^8y^8) is 9y^9x^8-8y^8x^7

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(\partial)/(\partial x)(x^9y^9-x^8y^8)

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

9 y^{9} x^{8} - 8 y^{8} x^{7}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x^{8} y^{8}) = 8 y^{8} x^{7}

= 9 y^{9} x^{8} - 8 y^{8} x^{7}

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What is (\partial)/(\partial x)(x^9y^9-x^8y^8) ?
The answer to (\partial)/(\partial x)(x^9y^9-x^8y^8) is 9y^9x^8-8y^8x^7