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

The answer to (\partial)/(\partial x)(x^4y-2x^3y^2) is 4yx^3-6y^2x^2

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

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

4 y x^{3} - 6 y^{2} x^{2}

Solution steps

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

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

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

= 4 y x^{3} - 6 y^{2} x^{2}

\int e \frac{x}{2} d x

x \to 3 + lim (\frac{3 - x}{∣ x - 3 ∣})

y^{^{'}} = ln (x)

f (t) = (1 + e^{4 t})^{2}

\int \frac{3 x + 1}{x ( x + 1 ) ^{2}} d x

What is (\partial)/(\partial x)(x^4y-2x^3y^2) ?
The answer to (\partial)/(\partial x)(x^4y-2x^3y^2) is 4yx^3-6y^2x^2