What is (\partial)/(\partial x)(x^4y-x^2y^3) ?

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

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(\partial)/(\partial x)(x^4y-x^2y^3)

\frac{\partial}{\partial x} (x^{4} y - x^{2} y^{3})

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

Solution steps

\frac{\partial}{\partial x} (x^{4} y - x^{2} y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 4 y x^{3} - 2 y^{3} x

d er i v a t i v e y = 3 x^{2} + \frac{4 x}{3} - 2

d er i v a t i v e \frac{3}{r ^{3}}

\frac{d y}{d x} = \frac{1 - y ^{2}}{x}

\int \frac{tan ^{3} ( \frac{2}{z} )}{z ^{2}}

\frac{d y}{d x} + x y = y^{4}

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