What is the derivative of x^2(2x-1^4) ?

The derivative of x^2(2x-1^4) is 2x(2x-1)^4+8(2x-1)^3x^2

What is the first derivative of x^2(2x-1^4) ?

The first derivative of x^2(2x-1^4) is 2x(2x-1)^4+8(2x-1)^3x^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x^{2} (2 x - 1)^{4})

2 x (2 x - 1)^{4} + 8 (2 x - 1)^{3} x^{2}

Solution steps

\frac{d}{d x} (x^{2} (2 x - 1)^{4})

Apply the Product Rule:

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

f = x^{2}, g = (2 x - 1)^{4}

= \frac{d}{d x} (x^{2}) (2 x - 1)^{4} + \frac{d}{d x} ((2 x - 1)^{4}) x^{2}

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

\frac{d}{d x} ((2 x - 1)^{4}) = 8 (2 x - 1)^{3}

= 2 x (2 x - 1)^{4} + 8 (2 x - 1)^{3} x^{2}

What is the derivative of x^2(2x-1^4) ?
The derivative of x^2(2x-1^4) is 2x(2x-1)^4+8(2x-1)^3x^2
What is the first derivative of x^2(2x-1^4) ?
The first derivative of x^2(2x-1^4) is 2x(2x-1)^4+8(2x-1)^3x^2