What is the derivative of x(6-x^{2/3}) ?

The derivative of x(6-x^{2/3}) is (-5x+18)/(3(6-x)^{1/3)}

What is the first derivative of x(6-x^{2/3}) ?

The first derivative of x(6-x^{2/3}) is (-5x+18)/(3(6-x)^{1/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (x (6 - x)^{\frac{2}{3}})

\frac{- 5 x + 18}{3 ( 6 - x ) ^{\frac{1}{3}}}

Solution steps

\frac{d}{d x} (x (6 - x)^{\frac{2}{3}})

Apply the Product Rule:

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

f = x, g = (6 - x)^{\frac{2}{3}}

= \frac{d x}{d x} (6 - x)^{\frac{2}{3}} + \frac{d}{d x} ((6 - x)^{\frac{2}{3}}) x

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

\frac{d}{d x} ((6 - x)^{\frac{2}{3}}) = - \frac{2}{3 ( 6 - x ) ^{\frac{1}{3}}}

= 1 \cdot (6 - x)^{\frac{2}{3}} + (- \frac{2}{3 ( 6 - x ) ^{\frac{1}{3}}}) x

Simplify

1 \cdot (6 - x)^{\frac{2}{3}} + (- \frac{2}{3 ( 6 - x ) ^{\frac{1}{3}}}) x : \frac{- 5 x + 18}{3 ( 6 - x ) ^{\frac{1}{3}}}

= \frac{- 5 x + 18}{3 ( 6 - x ) ^{\frac{1}{3}}}

\int \frac{x ^{2} - 4}{x ^{3}} d x

\frac{d}{d x} (x^{2} e^{2} + 2^{y}) = 5

4 x^{4} - 4 x^{2}, x^{2}

\frac{d}{d x} (\frac{x - 1}{2})

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

What is the derivative of x(6-x^{2/3}) ?
The derivative of x(6-x^{2/3}) is (-5x+18)/(3(6-x)^{1/3)}
What is the first derivative of x(6-x^{2/3}) ?
The first derivative of x(6-x^{2/3}) is (-5x+18)/(3(6-x)^{1/3)}