What is the derivative of 2x^3sqrt(x+1) ?

The derivative of 2x^3sqrt(x+1) is (7x^3+6x^2)/(sqrt(x+1))

What is the first derivative of 2x^3sqrt(x+1) ?

The first derivative of 2x^3sqrt(x+1) is (7x^3+6x^2)/(sqrt(x+1))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

2 x^{3} x + 1

\frac{7 x ^{3} + 6 x ^{2}}{x + 1}

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3}, g = x + 1

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

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

\frac{d}{d x} (x + 1) = \frac{1}{2 x + 1}

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

Simplify

2 (3 x^{2} x + 1 + \frac{1}{2 x + 1} x^{3}) : \frac{7 x ^{3} + 6 x ^{2}}{x + 1}

= \frac{7 x ^{3} + 6 x ^{2}}{x + 1}

What is the derivative of 2x^3sqrt(x+1) ?
The derivative of 2x^3sqrt(x+1) is (7x^3+6x^2)/(sqrt(x+1))
What is the first derivative of 2x^3sqrt(x+1) ?
The first derivative of 2x^3sqrt(x+1) is (7x^3+6x^2)/(sqrt(x+1))