What is the d/(dy)((x)(x^2+y^2+y-2x-y^3)) ?

The d/(dy)((x)(x^2+y^2+y-2x-y^3)) is x(-3y^2+2y+1)

What is the first d/(dy)((x)(x^2+y^2+y-2x-y^3)) ?

The first d/(dy)((x)(x^2+y^2+y-2x-y^3)) is x(-3y^2+2y+1)

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

x (- 3 y^{2} + 2 y + 1)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

= x (0 + 2 y + 1 - 0 - 3 y^{2})

Simplify

= x (- 3 y^{2} + 2 y + 1)

\frac{d}{d x} ((f (x)) (9 x^{2} + 11 x + 2))

(4 + 32) (- 3 + 5)

(8 x^{2} - 16 x + 16) e^{x}

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

(4 x - 8) (2 x + 3)

What is the d/(dy)((x)(x^2+y^2+y-2x-y^3)) ?
The d/(dy)((x)(x^2+y^2+y-2x-y^3)) is x(-3y^2+2y+1)
What is the first d/(dy)((x)(x^2+y^2+y-2x-y^3)) ?
The first d/(dy)((x)(x^2+y^2+y-2x-y^3)) is x(-3y^2+2y+1)