What is (\partial)/(\partial x)(5x^5y^4+7x^6y^8) ?

The answer to (\partial)/(\partial x)(5x^5y^4+7x^6y^8) is 25y^4x^4+42y^8x^5

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(\partial)/(\partial x)(5x^5y^4+7x^6y^8)

\frac{\partial}{\partial x} (5 x^{5} y^{4} + 7 x^{6} y^{8})

25 y^{4} x^{4} + 42 y^{8} x^{5}

Solution steps

\frac{\partial}{\partial x} (5 x^{5} y^{4} + 7 x^{6} y^{8})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{5} y^{4}) + \frac{\partial}{\partial x} (7 x^{6} y^{8})

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

\frac{\partial}{\partial x} (7 x^{6} y^{8}) = 42 y^{8} x^{5}

= 25 y^{4} x^{4} + 42 y^{8} x^{5}

What is (\partial)/(\partial x)(5x^5y^4+7x^6y^8) ?
The answer to (\partial)/(\partial x)(5x^5y^4+7x^6y^8) is 25y^4x^4+42y^8x^5