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

The derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12

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

The first derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12

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

4 x^{3} - 12 x^{2} + 6 x - 12

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + 3, g = x^{2} - 4 x

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

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

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

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

Simplify

2 x (x^{2} - 4 x) + (2 x - 4) (x^{2} + 3) : 4 x^{3} - 12 x^{2} + 6 x - 12

= 4 x^{3} - 12 x^{2} + 6 x - 12

What is the derivative of (x^2+3(x^2-4x)) ?
The derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12
What is the first derivative of (x^2+3(x^2-4x)) ?
The first derivative of (x^2+3(x^2-4x)) is 4x^3-12x^2+6x-12