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

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

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

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

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

3 x y^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d y} (x^{3}) = 0

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

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

Simplify

= 3 x y^{2}

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

(- y + 2 x) d y

e^{u^{3} (u - v^{2})}

(3 + 2) x

f (x) = \frac{( 4 x + 1 ) ^{3}}{( 2 x - 5 ) ^{4}}

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