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

The answer to (\partial)/(\partial x)(5x^5y^8+8x^6y^7) is 25y^8x^4+48y^7x^5

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

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

25 y^{8} x^{4} + 48 y^{7} x^{5}

Solution steps

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

\frac{\partial}{\partial x} (5 x^{5} y^{8}) = 25 y^{8} x^{4}

\frac{\partial}{\partial x} (8 x^{6} y^{7}) = 48 y^{7} x^{5}

= 25 y^{8} x^{4} + 48 y^{7} x^{5}

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What is (\partial)/(\partial x)(5x^5y^8+8x^6y^7) ?
The answer to (\partial)/(\partial x)(5x^5y^8+8x^6y^7) is 25y^8x^4+48y^7x^5