What is the derivative of-(81/(\sqrt[3]{x+5)}) ?

The derivative of-(81/(\sqrt[3]{x+5)}) is (27)/((x+5)^{4/3)}

What is the first derivative of-(81/(\sqrt[3]{x+5)}) ?

The first derivative of-(81/(\sqrt[3]{x+5)}) is (27)/((x+5)^{4/3)}

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\frac{27}{( x + 5 ) ^{\frac{4}{3}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

= - 81 \frac{d}{d x} ((x + 5)^{- \frac{1}{3}})

Apply the chain rule:

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

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

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

= - 81 (- \frac{1}{3 ( x + 5 ) ^{\frac{4}{3}}} \cdot 1)

Simplify

- 81 (- \frac{1}{3 ( x + 5 ) ^{\frac{4}{3}}} \cdot 1) : \frac{27}{( x + 5 ) ^{\frac{4}{3}}}

= \frac{27}{( x + 5 ) ^{\frac{4}{3}}}

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What is the derivative of-(81/(\sqrt[3]{x+5)}) ?
The derivative of-(81/(\sqrt[3]{x+5)}) is (27)/((x+5)^{4/3)}
What is the first derivative of-(81/(\sqrt[3]{x+5)}) ?
The first derivative of-(81/(\sqrt[3]{x+5)}) is (27)/((x+5)^{4/3)}