What is the first d/(dy)(x^2(y-x)) ?

The first d/(dy)(x^2(y-x)) is x^2

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d/(dy)(x^2(y-x))

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

x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

\frac{d y}{d y} = 1

\frac{d x}{d y} = 0

= x^{2} (1 - 0)

Simplify

= x^{2}