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

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

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

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

- x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= x (0 - 1)

Simplify

= - x

(t e^{t} + t e^{2 t})^{2}

- \frac{40 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

\frac{d}{d x} ((1 - x^{2}) arctan (x)) - x

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

\frac{( x + 2 ) ( x - 3 )}{x}