What is the derivative of xy^2-x^3y ?

The derivative of xy^2-x^3y is y^2+2xy(dy)/(dx)-3x^2y-x^3(dy)/(dx)

What is the first derivative of xy^2-x^3y ?

The first derivative of xy^2-x^3y is y^2+2xy(dy)/(dx)-3x^2y-x^3(dy)/(dx)

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

y^{2} + 2 x y \frac{d y}{d x} - 3 x^{2} y - x^{3} \frac{d y}{d x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x y^{2}) = y^{2} + 2 x y \frac{d y}{d x}

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

= y^{2} + 2 x y \frac{d y}{d x} - (3 x^{2} y + \frac{d y}{d x} x^{3})

Simplify

y^{2} + 2 x y \frac{d y}{d x} - (3 x^{2} y + \frac{d y}{d x} x^{3}) : y^{2} + 2 x y \frac{d y}{d x} - 3 x^{2} y - x^{3} \frac{d y}{d x}

= y^{2} + 2 x y \frac{d y}{d x} - 3 x^{2} y - x^{3} \frac{d y}{d x}

What is the derivative of xy^2-x^3y ?
The derivative of xy^2-x^3y is y^2+2xy(dy)/(dx)-3x^2y-x^3(dy)/(dx)
What is the first derivative of xy^2-x^3y ?
The first derivative of xy^2-x^3y is y^2+2xy(dy)/(dx)-3x^2y-x^3(dy)/(dx)