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

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

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

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

x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d y} (x^{2}) = 0

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

= x (0 + 1)

Simplify

= x

(e^{5 x} - 1) (4 - x^{2})

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\frac{2 ( 7 - 4 )}{3}