en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x+1^3(x-1)^2)

Solution

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

Solution

3 (x + 1)^{2} (x - 1)^{2} + 2 (x - 1) (x + 1)^{3}

Solution steps

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

Apply the Product Rule:

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

f = (x + 1)^{3}, g = (x - 1)^{2}

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

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

\frac{d}{d x} ((x - 1)^{2}) = 2 (x - 1)

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

Popular Examples

integral of e^{7x-5}

\int e^{7 x - 5} d x

derivative of sqrt(3u)derivative of

3 u

tangent of f(x)=2x^2-3x+1,(2,3)tangent of

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

derivative of (x+1/(x^2))

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

(\partial)/(\partial z)((xy)^z)

\frac{\partial}{\partial z} ((x y)^{z})

Frequently Asked Questions (FAQ)

What is the derivative of (x+1^3(x-1)^2) ?
The derivative of (x+1^3(x-1)^2) is 3(x+1)^2(x-1)^2+2(x-1)(x+1)^3
What is the first derivative of (x+1^3(x-1)^2) ?
The first derivative of (x+1^3(x-1)^2) is 3(x+1)^2(x-1)^2+2(x-1)(x+1)^3