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Popular >

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

Solution

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

Solution

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

Solution steps

\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

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

Simplify

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

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\frac{d}{d x} (ln (x^{3}))

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limit as x approaches infinity of (x)^{(ln(2))/(1+ln(x))}

x \to \infty lim ((x)^{\frac{l n ( 2 )}{1 + l n ( x )}})

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Frequently Asked Questions (FAQ)

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