What is the (sqrt(x^3))^' ?

The (sqrt(x^3))^' is (3sqrt(x))/2

What is the first (sqrt(x^3))^' ?

The first (sqrt(x^3))^' is (3sqrt(x))/2

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(x^{3})^{^{'}}

\frac{3 x}{2}

Solution steps

(x^{3})^{'}

Apply radical rule:

= (x^{\frac{3}{2}})^{^{'}}

Apply the Power Rule:

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

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

Simplify

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

= \frac{3 x}{2}

f (x) = x - 3

\int 2 x^{6} d x

\int e^{2} x cos (3 x) d x

\int x^{3} e^{x^{2}} d x

\frac{\partial}{\partial x} (sin (x y z^{3}))