What is the derivative of f(x)= 5/(\sqrt[3]{x)} ?

The derivative of f(x)= 5/(\sqrt[3]{x)} is -5/(3x^{4/3)}

What is the first derivative of f(x)= 5/(\sqrt[3]{x)} ?

The first derivative of f(x)= 5/(\sqrt[3]{x)} is -5/(3x^{4/3)}

derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

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

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

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What is the derivative of f(x)= 5/(\sqrt[3]{x)} ?
The derivative of f(x)= 5/(\sqrt[3]{x)} is -5/(3x^{4/3)}
What is the first derivative of f(x)= 5/(\sqrt[3]{x)} ?
The first derivative of f(x)= 5/(\sqrt[3]{x)} is -5/(3x^{4/3)}