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)}

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derivative of

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

\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}}}

x \to - 5 lim (4 x + 24)

\int \frac{5 x ^{2}}{x ^{2} + 6} d x

y^{^{'}} = \frac{6 x}{y}

\frac{d}{d y} ((\frac{1}{y ^{2}} - \frac{3}{y ^{4}}) (y + 5 y^{3}))

y^{^{''}} - y^{^{'}} - 2 y = 5 e^{- t}

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)}