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

The derivative of (3x^2+4^2(4x^2-8)^2) is 1152x^7-1152x^5-2816x^3+1024x

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

The first derivative of (3x^2+4^2(4x^2-8)^2) is 1152x^7-1152x^5-2816x^3+1024x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

1152 x^{7} - 1152 x^{5} - 2816 x^{3} + 1024 x

Solution steps

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

Apply the Product Rule:

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

f = (3 x^{2} + 4)^{2}, g = (4 x^{2} - 8)^{2}

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

\frac{d}{d x} ((3 x^{2} + 4)^{2}) = 12 x (3 x^{2} + 4)

\frac{d}{d x} ((4 x^{2} - 8)^{2}) = 16 x (4 x^{2} - 8)

= 12 x (3 x^{2} + 4) (4 x^{2} - 8)^{2} + 16 x (4 x^{2} - 8) (3 x^{2} + 4)^{2}

Simplify

12 x (3 x^{2} + 4) (4 x^{2} - 8)^{2} + 16 x (4 x^{2} - 8) (3 x^{2} + 4)^{2} : 1152 x^{7} - 1152 x^{5} - 2816 x^{3} + 1024 x

= 1152 x^{7} - 1152 x^{5} - 2816 x^{3} + 1024 x

What is the derivative of (3x^2+4^2(4x^2-8)^2) ?
The derivative of (3x^2+4^2(4x^2-8)^2) is 1152x^7-1152x^5-2816x^3+1024x
What is the first derivative of (3x^2+4^2(4x^2-8)^2) ?
The first derivative of (3x^2+4^2(4x^2-8)^2) is 1152x^7-1152x^5-2816x^3+1024x