What is the derivative of x(x-1^3) ?

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

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

\frac{d}{d x} (arctan (\frac{1 - x}{1 + x}))

\int_{0}^{3} (- x^{2} + x - 1) d x

\int_{1}^{16} \frac{1}{x} d x

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