What is the d/(dy)((x)(4x^2y^2)) ?

The d/(dy)((x)(4x^2y^2)) is 8x^3y

What is the first d/(dy)((x)(4x^2y^2)) ?

The first d/(dy)((x)(4x^2y^2)) is 8x^3y

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\frac{d}{d y} ((x) (4 x^{2} y^{2}))

8 x^{3} y

Solution steps

\frac{d}{d y} ((x) (4 x^{2} y^{2}))

Simplify

(x) (4 x^{2} y^{2}) : 4 x^{3} y^{2}

= \frac{d}{d y} (4 x^{3} y^{2})

Treat

x

as a constant

Take the constant out:

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

= 4 x^{3} \frac{d}{d y} (y^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 4 x^{3} \cdot 2 y^{2 - 1}

Simplify

= 8 x^{3} y

e^{- 10 \cdot (0.05 + 0.03 + 0.3)}

90 e^{- 0.08 \cdot \frac{1}{2}}

e^{- y} \cdot e^{- \frac{x}{y}}

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

What is the d/(dy)((x)(4x^2y^2)) ?
The d/(dy)((x)(4x^2y^2)) is 8x^3y
What is the first d/(dy)((x)(4x^2y^2)) ?
The first d/(dy)((x)(4x^2y^2)) is 8x^3y