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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

\frac{d}{d x} (1) = 0

= \frac{2}{3 ( x + 1 ) ^{\frac{1}{3}}} - \frac{2}{3 x ^{\frac{1}{3}}} + 0

Simplify

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

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