What is the derivative of x(7x+9^{1/3}) ?

The derivative of x(7x+9^{1/3}) is (28x+27)/(3(7x+9)^{2/3)}

What is the first derivative of x(7x+9^{1/3}) ?

The first derivative of x(7x+9^{1/3}) is (28x+27)/(3(7x+9)^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (x (7 x + 9)^{\frac{1}{3}})

\frac{28 x + 27}{3 ( 7 x + 9 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (x (7 x + 9)^{\frac{1}{3}})

Apply the Product Rule:

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

f = x, g = (7 x + 9)^{\frac{1}{3}}

= \frac{d x}{d x} (7 x + 9)^{\frac{1}{3}} + \frac{d}{d x} ((7 x + 9)^{\frac{1}{3}}) x

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

\frac{d}{d x} ((7 x + 9)^{\frac{1}{3}}) = \frac{7}{3 ( 7 x + 9 ) ^{\frac{2}{3}}}

= 1 \cdot (7 x + 9)^{\frac{1}{3}} + \frac{7}{3 ( 7 x + 9 ) ^{\frac{2}{3}}} x

Simplify

1 \cdot (7 x + 9)^{\frac{1}{3}} + \frac{7}{3 ( 7 x + 9 ) ^{\frac{2}{3}}} x : \frac{28 x + 27}{3 ( 7 x + 9 ) ^{\frac{2}{3}}}

= \frac{28 x + 27}{3 ( 7 x + 9 ) ^{\frac{2}{3}}}

What is the derivative of x(7x+9^{1/3}) ?
The derivative of x(7x+9^{1/3}) is (28x+27)/(3(7x+9)^{2/3)}
What is the first derivative of x(7x+9^{1/3}) ?
The first derivative of x(7x+9^{1/3}) is (28x+27)/(3(7x+9)^{2/3)}