What is the derivative of (4sqrt(2)/3 x^{3/2}-1) ?

The derivative of (4sqrt(2)/3 x^{3/2}-1) is 2sqrt(2)x^{1/2}

What is the first derivative of (4sqrt(2)/3 x^{3/2}-1) ?

The first derivative of (4sqrt(2)/3 x^{3/2}-1) is 2sqrt(2)x^{1/2}

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\frac{d}{d x} (\frac{4 2}{3} x^{\frac{3}{2}} - 1)

22 x^{\frac{1}{2}}

Solution steps

\frac{d}{d x} (\frac{4 2}{3} x^{\frac{3}{2}} - 1)

Simplify

\frac{4 2}{3} x^{\frac{3}{2}} - 1 : \frac{4 2 x ^{\frac{3}{2}}}{3} - 1

= \frac{d}{d x} (\frac{4 2 x ^{\frac{3}{2}}}{3} - 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{4 2 x ^{\frac{3}{2}}}{3}) - \frac{d}{d x} (1)

\frac{d}{d x} (\frac{4 2 x ^{\frac{3}{2}}}{3}) = 22 x^{\frac{1}{2}}

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

= 22 x^{\frac{1}{2}} - 0

Simplify

= 22 x^{\frac{1}{2}}

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

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What is the derivative of (4sqrt(2)/3 x^{3/2}-1) ?
The derivative of (4sqrt(2)/3 x^{3/2}-1) is 2sqrt(2)x^{1/2}
What is the first derivative of (4sqrt(2)/3 x^{3/2}-1) ?
The first derivative of (4sqrt(2)/3 x^{3/2}-1) is 2sqrt(2)x^{1/2}