What is the derivative of 3x^4(2x^2-1) ?

The derivative of 3x^4(2x^2-1) is 3(12x^5-4x^3)

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

The first derivative of 3x^4(2x^2-1) is 3(12x^5-4x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

3 (12 x^{5} - 4 x^{3})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

3 (4 x^{3} (2 x^{2} - 1) + 4 x x^{4}) : 3 (12 x^{5} - 4 x^{3})

= 3 (12 x^{5} - 4 x^{3})

What is the derivative of 3x^4(2x^2-1) ?
The derivative of 3x^4(2x^2-1) is 3(12x^5-4x^3)
What is the first derivative of 3x^4(2x^2-1) ?
The first derivative of 3x^4(2x^2-1) is 3(12x^5-4x^3)