What is the derivative of (6-x^{1/3}) ?

The derivative of (6-x^{1/3}) is -1/(3(6-x)^{2/3)}

What is the first derivative of (6-x^{1/3}) ?

The first derivative of (6-x^{1/3}) is -1/(3(6-x)^{2/3)}

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\frac{d}{d x} ((6 - x)^{\frac{1}{3}})

- \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} ((6 - x)^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}} \frac{d}{d x} (6 - x)

= \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}} \frac{d}{d x} (6 - x)

\frac{d}{d x} (6 - x) = - 1

= \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}} (- 1)

Simplify

= - \frac{1}{3 ( 6 - x ) ^{\frac{2}{3}}}

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What is the derivative of (6-x^{1/3}) ?
The derivative of (6-x^{1/3}) is -1/(3(6-x)^{2/3)}
What is the first derivative of (6-x^{1/3}) ?
The first derivative of (6-x^{1/3}) is -1/(3(6-x)^{2/3)}