What is (\partial)/(\partial x)(x^6y^6+9x^4y) ?

The answer to (\partial)/(\partial x)(x^6y^6+9x^4y) is 6y^6x^5+36yx^3

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(\partial)/(\partial x)(x^6y^6+9x^4y)

\frac{\partial}{\partial x} (x^{6} y^{6} + 9 x^{4} y)

6 y^{6} x^{5} + 36 y x^{3}

Solution steps

\frac{\partial}{\partial x} (x^{6} y^{6} + 9 x^{4} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6} y^{6}) + \frac{\partial}{\partial x} (9 x^{4} y)

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

\frac{\partial}{\partial x} (9 x^{4} y) = 36 y x^{3}

= 6 y^{6} x^{5} + 36 y x^{3}

What is (\partial)/(\partial x)(x^6y^6+9x^4y) ?
The answer to (\partial)/(\partial x)(x^6y^6+9x^4y) is 6y^6x^5+36yx^3