What is the derivative of f(x)= 9/(\sqrt[5]{x)} ?

The derivative of f(x)= 9/(\sqrt[5]{x)} is -9/(5x^{6/5)}

What is the first derivative of f(x)= 9/(\sqrt[5]{x)} ?

The first derivative of f(x)= 9/(\sqrt[5]{x)} is -9/(5x^{6/5)}

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derivative of

f (x) = \frac{9}{5 x}

- \frac{9}{5 x ^{\frac{6}{5}}}

Solution steps

\frac{d}{d x} (\frac{9}{5 x})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{5 x})

Apply exponent rule:

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

= 9 \frac{d}{d x} (x^{- \frac{1}{5}})

Apply the Power Rule:

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

= 9 (- \frac{1}{5} x^{- \frac{1}{5} - 1})

Simplify

9 (- \frac{1}{5} x^{- \frac{1}{5} - 1}) : - \frac{9}{5 x ^{\frac{6}{5}}}

= - \frac{9}{5 x ^{\frac{6}{5}}}

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What is the derivative of f(x)= 9/(\sqrt[5]{x)} ?
The derivative of f(x)= 9/(\sqrt[5]{x)} is -9/(5x^{6/5)}
What is the first derivative of f(x)= 9/(\sqrt[5]{x)} ?
The first derivative of f(x)= 9/(\sqrt[5]{x)} is -9/(5x^{6/5)}