What is (\partial)/(\partial x)(x^8y^8-x^7y^7) ?

The answer to (\partial)/(\partial x)(x^8y^8-x^7y^7) is 8y^8x^7-7y^7x^6

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(\partial)/(\partial x)(x^8y^8-x^7y^7)

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

8 y^{8} x^{7} - 7 y^{7} x^{6}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 8 y^{8} x^{7} - 7 y^{7} x^{6}

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What is (\partial)/(\partial x)(x^8y^8-x^7y^7) ?
The answer to (\partial)/(\partial x)(x^8y^8-x^7y^7) is 8y^8x^7-7y^7x^6