What is (\partial)/(\partial x)(7x^5y^7+3x^8y^6) ?

The answer to (\partial)/(\partial x)(7x^5y^7+3x^8y^6) is 35y^7x^4+24y^6x^7

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(\partial)/(\partial x)(7x^5y^7+3x^8y^6)

\frac{\partial}{\partial x} (7 x^{5} y^{7} + 3 x^{8} y^{6})

35 y^{7} x^{4} + 24 y^{6} x^{7}

Solution steps

\frac{\partial}{\partial x} (7 x^{5} y^{7} + 3 x^{8} y^{6})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (7 x^{5} y^{7}) + \frac{\partial}{\partial x} (3 x^{8} y^{6})

\frac{\partial}{\partial x} (7 x^{5} y^{7}) = 35 y^{7} x^{4}

\frac{\partial}{\partial x} (3 x^{8} y^{6}) = 24 y^{6} x^{7}

= 35 y^{7} x^{4} + 24 y^{6} x^{7}

What is (\partial)/(\partial x)(7x^5y^7+3x^8y^6) ?
The answer to (\partial)/(\partial x)(7x^5y^7+3x^8y^6) is 35y^7x^4+24y^6x^7