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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = \frac{2 x}{x ^{2} + 4}

\int - 9 x^{2} sec (3 x^{3} + 1) tan (3 x^{3} + 1) d x

\int in x d x

\frac{\partial}{\partial x} (y f (x) + 2 x^{3})

e^{1 - x} \cdot (5 - x^{2})

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