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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of 6(x-3)^{2/3} ?
The derivative of 6(x-3)^{2/3} is 4/((x-3)^{1/3)}
What is the first derivative of 6(x-3)^{2/3} ?
The first derivative of 6(x-3)^{2/3} is 4/((x-3)^{1/3)}