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

The answer to (\partial)/(\partial x)(x^4y-4x^3y^2) is 4yx^3-12y^2x^2

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

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

4 y x^{3} - 12 y^{2} x^{2}

Solution steps

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

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

\frac{\partial}{\partial x} (4 x^{3} y^{2}) = 12 y^{2} x^{2}

= 4 y x^{3} - 12 y^{2} x^{2}

\int (\frac{3 x}{2} - \frac{9}{4}) e^{x (x - 3)} d x

f (x) = 1 - 2 tan (x), at x = \frac{3 π}{4}

y = x^{3} - 15 x

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

\frac{d}{d x} (e^{k t a n (5 x)})

What is (\partial)/(\partial x)(x^4y-4x^3y^2) ?
The answer to (\partial)/(\partial x)(x^4y-4x^3y^2) is 4yx^3-12y^2x^2