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

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

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

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

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

2 x^{2} y

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= x (0 + 2 x y)

Simplify

x (0 + 2 x y) : 2 x^{2} y

= 2 x^{2} y

\frac{t + 10}{( t + 1 ) ( t ^{2} - 1 )}

π (10 x + 9)^{2}

3 (x + 7 = 2 (2 x + 5))

\frac{10 s + 1}{s ( s + 4 )}

\frac{x ( x ^{2} - 1 )}{x + 5}

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