What is (\partial)/(\partial x)(x^6+8xy^5) ?

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

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(\partial)/(\partial x)(x^6+8xy^5)

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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