What is (\partial)/(\partial x)((x+1)^2(x^2+2x)) ?

The answer to (\partial)/(\partial x)((x+1)^2(x^2+2x)) is 4x^3+12x^2+10x+2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((x+1)^2(x^2+2x))

\frac{\partial}{\partial x} ((x + 1)^{2} (x^{2} + 2 x))

4 x^{3} + 12 x^{2} + 10 x + 2

Solution steps

\frac{\partial}{\partial x} ((x + 1)^{2} (x^{2} + 2 x))

Apply the Product Rule:

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

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

= \frac{\partial}{\partial x} ((x + 1)^{2}) (x^{2} + 2 x) + \frac{\partial}{\partial x} (x^{2} + 2 x) (x + 1)^{2}

\frac{\partial}{\partial x} ((x + 1)^{2}) = 2 (x + 1)

\frac{\partial}{\partial x} (x^{2} + 2 x) = 2 x + 2

= 2 (x + 1) (x^{2} + 2 x) + (2 x + 2) (x + 1)^{2}

Simplify

2 (x + 1) (x^{2} + 2 x) + (2 x + 2) (x + 1)^{2} : 4 x^{3} + 12 x^{2} + 10 x + 2

= 4 x^{3} + 12 x^{2} + 10 x + 2

f (x) = \frac{x ^{3} - 1 x ^{2} + 2}{x ^{2}}

\int (x x + 3) d x

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

13 + 2 x - x^{2}, 3 x + 1

f (x) = (x + 1)^{2 x}

What is (\partial)/(\partial x)((x+1)^2(x^2+2x)) ?
The answer to (\partial)/(\partial x)((x+1)^2(x^2+2x)) is 4x^3+12x^2+10x+2