What is the derivative of x(1-x^6) ?

The derivative of x(1-x^6) is (1-x)^6-6x(1-x)^5

What is the first derivative of x(1-x^6) ?

The first derivative of x(1-x^6) is (1-x)^6-6x(1-x)^5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x (1 - x)^{6})

(1 - x)^{6} - 6 x (1 - x)^{5}

Solution steps

\frac{d}{d x} (x (1 - x)^{6})

Apply the Product Rule:

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

f = x, g = (1 - x)^{6}

= \frac{d x}{d x} (1 - x)^{6} + \frac{d}{d x} ((1 - x)^{6}) x

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

\frac{d}{d x} ((1 - x)^{6}) = - 6 (1 - x)^{5}

= 1 \cdot (1 - x)^{6} + (- 6 (1 - x)^{5}) x

Simplify

= (1 - x)^{6} - 6 x (1 - x)^{5}

\int ln (2 x) (x) d x

\int tan^{2} (x) d x

\int cot (x) csc^{3} (x) d x

\frac{\partial}{\partial x} (sin (\frac{x \cdot y}{y - 4}))

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

What is the derivative of x(1-x^6) ?
The derivative of x(1-x^6) is (1-x)^6-6x(1-x)^5
What is the first derivative of x(1-x^6) ?
The first derivative of x(1-x^6) is (1-x)^6-6x(1-x)^5