What is the d/(dy)((x)(-5x^2+20x+2)) ?

The d/(dy)((x)(-5x^2+20x+2)) is -15y^2+40y+2

What is the first d/(dy)((x)(-5x^2+20x+2)) ?

The first d/(dy)((x)(-5x^2+20x+2)) is -15y^2+40y+2

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\frac{d}{d y} ((y) (- 5 y^{2} + 20 y + 2))

- 15 y^{2} + 40 y + 2

Solution steps

\frac{d}{d y} ((y) (- 5 y^{2} + 20 y + 2))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = - 5 y^{2} + 20 y + 2

= \frac{d y}{d y} (- 5 y^{2} + 20 y + 2) + \frac{d}{d y} (- 5 y^{2} + 20 y + 2) y

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

\frac{d}{d y} (- 5 y^{2} + 20 y + 2) = - 10 y + 20

= 1 \cdot (- 5 y^{2} + 20 y + 2) + (- 10 y + 20) y

Simplify

1 \cdot (- 5 y^{2} + 20 y + 2) + (- 10 y + 20) y : - 15 y^{2} + 40 y + 2

= - 15 y^{2} + 40 y + 2

2^{4}

\frac{2 ( - 8 x ^{3} + 72 x ^{2} - 216 x + 216 )}{27}

x e^{x} (x e^{x} - 1)

(3 e^{5 t} - 2 e^{4 t}) (15 e^{5 t} - 8 e^{4 t})

What is the d/(dy)((x)(-5x^2+20x+2)) ?
The d/(dy)((x)(-5x^2+20x+2)) is -15y^2+40y+2
What is the first d/(dy)((x)(-5x^2+20x+2)) ?
The first d/(dy)((x)(-5x^2+20x+2)) is -15y^2+40y+2