What is the derivative of f(x)= 5/4 x^{4/3} ?

The derivative of f(x)= 5/4 x^{4/3} is (5x^{1/3})/3

What is the first derivative of f(x)= 5/4 x^{4/3} ?

The first derivative of f(x)= 5/4 x^{4/3} is (5x^{1/3})/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{5}{4} x^{\frac{4}{3}}

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

= \frac{5 x ^{\frac{1}{3}}}{3}

What is the derivative of f(x)= 5/4 x^{4/3} ?
The derivative of f(x)= 5/4 x^{4/3} is (5x^{1/3})/3
What is the first derivative of f(x)= 5/4 x^{4/3} ?
The first derivative of f(x)= 5/4 x^{4/3} is (5x^{1/3})/3