What is the d/(dy)((x)(1+2x)^6) ?

The d/(dy)((x)(1+2x)^6) is (1+2y)^6+12y(1+2y)^5

What is the first d/(dy)((x)(1+2x)^6) ?

The first d/(dy)((x)(1+2x)^6) is (1+2y)^6+12y(1+2y)^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d y} ((y) (1 + 2 y)^{6})

(1 + 2 y)^{6} + 12 y (1 + 2 y)^{5}

Solution steps

\frac{d}{d y} ((y) (1 + 2 y)^{6})

Apply the Product Rule:

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

f = y, g = (1 + 2 y)^{6}

= \frac{d y}{d y} (1 + 2 y)^{6} + \frac{d}{d y} ((1 + 2 y)^{6}) y

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

\frac{d}{d y} ((1 + 2 y)^{6}) = 12 (1 + 2 y)^{5}

= 1 \cdot (1 + 2 y)^{6} + 12 (1 + 2 y)^{5} y

Simplify

= (1 + 2 y)^{6} + 12 y (1 + 2 y)^{5}

(3 - \frac{3}{2} y)^{3}

- x (x^{3} + y) d y

(x - 1 - 3) (x - 1 + 3)

(3 + 2 i)^{5}

(x - 32)^{2}

What is the d/(dy)((x)(1+2x)^6) ?
The d/(dy)((x)(1+2x)^6) is (1+2y)^6+12y(1+2y)^5
What is the first d/(dy)((x)(1+2x)^6) ?
The first d/(dy)((x)(1+2x)^6) is (1+2y)^6+12y(1+2y)^5