What is (\partial)/(\partial x)(5x^8y^5+2x^4y^6) ?

The answer to (\partial)/(\partial x)(5x^8y^5+2x^4y^6) is 40y^5x^7+8y^6x^3

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(\partial)/(\partial x)(5x^8y^5+2x^4y^6)

\frac{\partial}{\partial x} (5 x^{8} y^{5} + 2 x^{4} y^{6})

40 y^{5} x^{7} + 8 y^{6} x^{3}

Solution steps

\frac{\partial}{\partial x} (5 x^{8} y^{5} + 2 x^{4} y^{6})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x^{8} y^{5}) + \frac{\partial}{\partial x} (2 x^{4} y^{6})

\frac{\partial}{\partial x} (5 x^{8} y^{5}) = 40 y^{5} x^{7}

\frac{\partial}{\partial x} (2 x^{4} y^{6}) = 8 y^{6} x^{3}

= 40 y^{5} x^{7} + 8 y^{6} x^{3}

What is (\partial)/(\partial x)(5x^8y^5+2x^4y^6) ?
The answer to (\partial)/(\partial x)(5x^8y^5+2x^4y^6) is 40y^5x^7+8y^6x^3