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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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