What is (\partial)/(\partial x)(2xy^7+x^8y^7) ?

The answer to (\partial)/(\partial x)(2xy^7+x^8y^7) is 2y^7+8y^7x^7

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(\partial)/(\partial x)(2xy^7+x^8y^7)

\frac{\partial}{\partial x} (2 x y^{7} + x^{8} y^{7})

2 y^{7} + 8 y^{7} x^{7}

Solution steps

\frac{\partial}{\partial x} (2 x y^{7} + x^{8} y^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x y^{7}) + \frac{\partial}{\partial x} (x^{8} y^{7})

\frac{\partial}{\partial x} (2 x y^{7}) = 2 y^{7}

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

= 2 y^{7} + 8 y^{7} x^{7}

What is (\partial)/(\partial x)(2xy^7+x^8y^7) ?
The answer to (\partial)/(\partial x)(2xy^7+x^8y^7) is 2y^7+8y^7x^7