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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

\int e^{- 0.01 x} d x

10 sin^{2} (x) + 10 cos^{2} (x)

e^{- 4 x}

\frac{d}{d x} (\frac{8 x}{8 + x})

\frac{1}{2 x} y^{^{'}} = \frac{x}{3 y}

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