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

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

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

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

2 y x - y^{3}

Solution steps

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

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

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

= 2 y x - y^{3}

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

\int 100 q^{- 0.5} d q

\int \frac{x ^{5}}{x ^{6} + 3} d x

24 x

f (x) = \frac{x - 1}{x + 1}

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