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

The answer to (\partial)/(\partial x)(4x^8y^6+6x^7y^5) is 32y^6x^7+42y^5x^6

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

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

32 y^{6} x^{7} + 42 y^{5} x^{6}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{8} y^{6}) = 32 y^{6} x^{7}

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

= 32 y^{6} x^{7} + 42 y^{5} x^{6}

What is (\partial)/(\partial x)(4x^8y^6+6x^7y^5) ?
The answer to (\partial)/(\partial x)(4x^8y^6+6x^7y^5) is 32y^6x^7+42y^5x^6