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

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

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

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

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derivative of

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