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

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

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(\partial)/(\partial x)(x^3y-xy^3)

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

3 y x^{2} - y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 y x^{2} - y^{3}

(- 12 x y^{2} - 12 y) + (- 12 x^{2} y - 12 x) y^{^{'}} = 0

\int e^{- 4 x} d x

\int \frac{( x ^{10} )}{x ^{2} + x - 2} d x

f (x) = \frac{4}{x}, at x = 3

\frac{1}{4 s ^{2} + 1}

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