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

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

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

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

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

Solution steps

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

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

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

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

y = x + 4, y = x^{2} + x - 12

2 (x + 1), 3 (x + 1), x = 4

x^{3} + x + 3

e^{x}, e^{- 4 x}, x = ln (3)

\int_{1}^{3} ((x)^{3} + e^{- 3 x}) d x

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