What is the d/(dy)((x)(x^3+3y^3+5x+y)) ?

The d/(dy)((x)(x^3+3y^3+5x+y)) is x(9y^2+1)

What is the first d/(dy)((x)(x^3+3y^3+5x+y)) ?

The first d/(dy)((x)(x^3+3y^3+5x+y)) is x(9y^2+1)

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\frac{d}{d y} ((x) (x^{3} + 3 y^{3} + 5 x + y))

x (9 y^{2} + 1)

Solution steps

\frac{d}{d y} ((x) (x^{3} + 3 y^{3} + 5 x + y))

Treat

x

as a constant

Take the constant out:

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

= x \frac{d}{d y} (x^{3} + 3 y^{3} + 5 x + y)

Apply the Sum/Difference Rule:

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

= x (\frac{d}{d y} (x^{3}) + \frac{d}{d y} (3 y^{3}) + \frac{d}{d y} (5 x) + \frac{d y}{d y})

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

\frac{d}{d y} (3 y^{3}) = 9 y^{2}

\frac{d}{d y} (5 x) = 0

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

= x (0 + 9 y^{2} + 0 + 1)

Simplify

= x (9 y^{2} + 1)

e^{- s t} \cdot t \cdot (e^{i t} + e^{- i t})

2 π (\frac{9 π}{4} - 36)

\frac{32 ( x + 1 )}{27}

(3 x^{2} - 5)^{2} d x

x^{2} \cdot x^{1}

What is the d/(dy)((x)(x^3+3y^3+5x+y)) ?
The d/(dy)((x)(x^3+3y^3+5x+y)) is x(9y^2+1)
What is the first d/(dy)((x)(x^3+3y^3+5x+y)) ?
The first d/(dy)((x)(x^3+3y^3+5x+y)) is x(9y^2+1)