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

The answer to (\partial)/(\partial x)(x^6y^8+7x^7y) is 6y^8x^5+49yx^6

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

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

6 y^{8} x^{5} + 49 y x^{6}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (7 x^{7} y) = 49 y x^{6}

= 6 y^{8} x^{5} + 49 y x^{6}

What is (\partial)/(\partial x)(x^6y^8+7x^7y) ?
The answer to (\partial)/(\partial x)(x^6y^8+7x^7y) is 6y^8x^5+49yx^6