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

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

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

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

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

\int \frac{1}{x 1 - x ^{2}} d x

f (x) = \frac{1 - 3 x}{6 + x}

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

\frac{d y}{d x} = \frac{( 3 y + 10507 )}{x - 12}, y (0) = 47

y = arcsec (x)

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