What is the derivative of 3x^{1/3}-5x^{4/3} ?

The derivative of 3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}

What is the first derivative of 3x^{1/3}-5x^{4/3} ?

The first derivative of 3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}}

\frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (3 x^{\frac{1}{3}} - 5 x^{\frac{4}{3}})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 x^{\frac{1}{3}}) - \frac{d}{d x} (5 x^{\frac{4}{3}})

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

\frac{d}{d x} (5 x^{\frac{4}{3}}) = \frac{20 x ^{\frac{1}{3}}}{3}

= \frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3}

Simplify

\frac{1}{x ^{\frac{2}{3}}} - \frac{20 x ^{\frac{1}{3}}}{3} : \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

= \frac{3 - 20 x}{3 x ^{\frac{2}{3}}}

What is the derivative of 3x^{1/3}-5x^{4/3} ?
The derivative of 3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}
What is the first derivative of 3x^{1/3}-5x^{4/3} ?
The first derivative of 3x^{1/3}-5x^{4/3} is (3-20x)/(3x^{2/3)}