What is the d/(dy)((x)(x(2x+3)^4)) ?

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

What is the first d/(dy)((x)(x(2x+3)^4)) ?

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

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

2 y (2 y + 3)^{4} + 8 (2 y + 3)^{3} y^{2}

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = y^{2}, g = (2 y + 3)^{4}

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

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

\frac{d}{d y} ((2 y + 3)^{4}) = 8 (2 y + 3)^{3}

= 2 y (2 y + 3)^{4} + 8 (2 y + 3)^{3} y^{2}

(4 x + 1) e^{5 x}

(x - 0.5 y + 1 = 0,) (2 x - y + 6 = 0)

ln (x) (x^{2} - 1)

(2 + 3 x - 4 x^{2})^{5}

- 8 d + (- 1) + 9 d^{2} + 8 d

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