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}

\frac{d}{d x} ((4 x^{3} + 5 x^{2}) (9 x))

y = 2 x^{2} - 3 x, (2, 2)

x \to 2 - lim (\frac{x + 2}{x - 2})

y = x - 2

x \to 1 lim (x^{2} + e^{x})

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