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

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

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

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

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

x (y^{2} - 1)

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

= x (y^{2} - 1)

x^{\frac{1}{3}} (1 - 2 x) d x

\frac{( x e ^{x} )}{x ^{2}}

a (3, - 1) b (3, 7)

(1 + 2 e^{\frac{x}{y}}) d x + 2 e^{\frac{x}{y}} (1 - \frac{x}{y}) d y

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

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