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

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

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

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

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

- x

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply radical rule:

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

= - x

\int_{- 1}^{4} (3 x^{2} + 8 x - 5) d x

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

f (x) = \frac{4}{1 + x ^{2}}

\int x^{2} \cdot e^{2 x} d x

y^{^{'}} = 1 + x - y - x y

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