What is the derivative of (3x^3+9x^2/x) ?

The derivative of (3x^3+9x^2/x) is 3(2x+3)

What is the first derivative of (3x^3+9x^2/x) ?

The first derivative of (3x^3+9x^2/x) is 3(2x+3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{3 x ^{3} + 9 x ^{2}}{x})

3 (2 x + 3)

Solution steps

\frac{d}{d x} (\frac{3 x ^{3} + 9 x ^{2}}{x})

Simplify

\frac{3 x ^{3} + 9 x ^{2}}{x} : 3 x (x + 3)

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = x + 3

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

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

\frac{d}{d x} (x + 3) = 1

= 3 (1 \cdot (x + 3) + 1 \cdot x)

Simplify

3 (1 \cdot (x + 3) + 1 \cdot x) : 3 (2 x + 3)

= 3 (2 x + 3)

What is the derivative of (3x^3+9x^2/x) ?
The derivative of (3x^3+9x^2/x) is 3(2x+3)
What is the first derivative of (3x^3+9x^2/x) ?
The first derivative of (3x^3+9x^2/x) is 3(2x+3)