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

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

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

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

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Popular >

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{7}{ln ( x )}

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

\int (4 x^{3} + 3 x^{2} + 2 x + 1) d x

\frac{1}{t}

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

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