What is the derivative of x(2x+7)^{1/3} ?

The derivative of x(2x+7)^{1/3} is (8x+21)/(3(2x+7)^{2/3)}

What is the first derivative of x(2x+7)^{1/3} ?

The first derivative of x(2x+7)^{1/3} is (8x+21)/(3(2x+7)^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

\frac{8 x + 21}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (2 x + 7)^{\frac{1}{3}}

= \frac{d x}{d x} (2 x + 7)^{\frac{1}{3}} + \frac{d}{d x} ((2 x + 7)^{\frac{1}{3}}) x

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

\frac{d}{d x} ((2 x + 7)^{\frac{1}{3}}) = \frac{2}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

= 1 \cdot (2 x + 7)^{\frac{1}{3}} + \frac{2}{3 ( 2 x + 7 ) ^{\frac{2}{3}}} x

Simplify

1 \cdot (2 x + 7)^{\frac{1}{3}} + \frac{2}{3 ( 2 x + 7 ) ^{\frac{2}{3}}} x : \frac{8 x + 21}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

= \frac{8 x + 21}{3 ( 2 x + 7 ) ^{\frac{2}{3}}}

What is the derivative of x(2x+7)^{1/3} ?
The derivative of x(2x+7)^{1/3} is (8x+21)/(3(2x+7)^{2/3)}
What is the first derivative of x(2x+7)^{1/3} ?
The first derivative of x(2x+7)^{1/3} is (8x+21)/(3(2x+7)^{2/3)}