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

The answer to (\partial)/(\partial x)(x^6y-3x^3y^2) is 6yx^5-9y^2x^2

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

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

6 y x^{5} - 9 y^{2} x^{2}

Solution steps

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

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

\frac{\partial}{\partial x} (3 x^{3} y^{2}) = 9 y^{2} x^{2}

= 6 y x^{5} - 9 y^{2} x^{2}

\int \frac{1}{9 x ^{2} + 4} d x

(x - 6)^{\frac{8}{9}}

y = \frac{1 - cos ( x )}{sin ( x )}

y^{^{''}} + 16 y^{^{'}} + 64 y = t^{2} e^{- 8 t} - e^{- 8 t}

\frac{\partial}{\partial y} (6 x e^{x^{2} + y^{2}})

What is (\partial)/(\partial x)(x^6y-3x^3y^2) ?
The answer to (\partial)/(\partial x)(x^6y-3x^3y^2) is 6yx^5-9y^2x^2