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

The derivative of x^4(x^2-2x^2) is 8x^7-28x^6+24x^5

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

The first derivative of x^4(x^2-2x^2) is 8x^7-28x^6+24x^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^{4} (x^{2} - 2 x)^{2})

8 x^{7} - 28 x^{6} + 24 x^{5}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

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

Simplify

4 x^{3} (x^{2} - 2 x)^{2} + 2 (x^{2} - 2 x) (2 x - 2) x^{4} : 8 x^{7} - 28 x^{6} + 24 x^{5}

= 8 x^{7} - 28 x^{6} + 24 x^{5}

What is the derivative of x^4(x^2-2x^2) ?
The derivative of x^4(x^2-2x^2) is 8x^7-28x^6+24x^5
What is the first derivative of x^4(x^2-2x^2) ?
The first derivative of x^4(x^2-2x^2) is 8x^7-28x^6+24x^5