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

The answer to (\partial)/(\partial x)(x^7y^8-x^6y^7) is 7y^8x^6-6y^7x^5

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(\partial)/(\partial x)(x^7y^8-x^6y^7)

\frac{\partial}{\partial x} (x^{7} y^{8} - x^{6} y^{7})

7 y^{8} x^{6} - 6 y^{7} x^{5}

Solution steps

\frac{\partial}{\partial x} (x^{7} y^{8} - x^{6} y^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{7} y^{8}) - \frac{\partial}{\partial x} (x^{6} y^{7})

\frac{\partial}{\partial x} (x^{7} y^{8}) = 7 y^{8} x^{6}

\frac{\partial}{\partial x} (x^{6} y^{7}) = 6 y^{7} x^{5}

= 7 y^{8} x^{6} - 6 y^{7} x^{5}

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What is (\partial)/(\partial x)(x^7y^8-x^6y^7) ?
The answer to (\partial)/(\partial x)(x^7y^8-x^6y^7) is 7y^8x^6-6y^7x^5