What is the derivative of 2/(\sqrt[3]{x-1}) ?

The derivative of 2/(\sqrt[3]{x-1}) is -2/(3(x-1)^{4/3)}

What is the first derivative of 2/(\sqrt[3]{x-1}) ?

The first derivative of 2/(\sqrt[3]{x-1}) is -2/(3(x-1)^{4/3)}

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- \frac{2}{3 ( x - 1 ) ^{\frac{4}{3}}}

Solution steps

Take the constant out:

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

Apply exponent rule:

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

= 2 \frac{d}{d x} ((x - 1)^{- \frac{1}{3}})

Apply the chain rule:

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

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

\frac{d}{d x} (x - 1) = 1

= 2 (- \frac{1}{3 ( x - 1 ) ^{\frac{4}{3}}} \cdot 1)

Simplify

2 (- \frac{1}{3 ( x - 1 ) ^{\frac{4}{3}}} \cdot 1) : - \frac{2}{3 ( x - 1 ) ^{\frac{4}{3}}}

= - \frac{2}{3 ( x - 1 ) ^{\frac{4}{3}}}

\frac{1}{3 x + 5}

\int - 25 cos (- 5 t) d t

x \to - 1 lim (\frac{2}{x + 1})

2^{t^{3}}

\frac{d}{d x} (\frac{x ^{2} - 2 x}{x ^{2} + 5 x})

What is the derivative of 2/(\sqrt[3]{x-1}) ?
The derivative of 2/(\sqrt[3]{x-1}) is -2/(3(x-1)^{4/3)}
What is the first derivative of 2/(\sqrt[3]{x-1}) ?
The first derivative of 2/(\sqrt[3]{x-1}) is -2/(3(x-1)^{4/3)}