What is (\partial)/(\partial x)(x^6y-3x^5y^2) ?

The answer to (\partial)/(\partial x)(x^6y-3x^5y^2) is 6yx^5-15y^2x^4

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(\partial)/(\partial x)(x^6y-3x^5y^2)

\frac{\partial}{\partial x} (x^{6} y - 3 x^{5} y^{2})

6 y x^{5} - 15 y^{2} x^{4}

Solution steps

\frac{\partial}{\partial x} (x^{6} y - 3 x^{5} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6} y) - \frac{\partial}{\partial x} (3 x^{5} y^{2})

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

\frac{\partial}{\partial x} (3 x^{5} y^{2}) = 15 y^{2} x^{4}

= 6 y x^{5} - 15 y^{2} x^{4}

\frac{\partial}{\partial x} (x (3 - 2 x - y))

\int e^{x} + 5 d x

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

What is (\partial)/(\partial x)(x^6y-3x^5y^2) ?
The answer to (\partial)/(\partial x)(x^6y-3x^5y^2) is 6yx^5-15y^2x^4