What is the (x^{3/2})^' ?

The (x^{3/2})^' is (3x^{1/2})/2

What is the first (x^{3/2})^' ?

The first (x^{3/2})^' is (3x^{1/2})/2

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

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

Solution steps

(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 ^{\frac{1}{2}}}{2}

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

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

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

y^{^{'}} = 1 + 9 x - 5 y, y (1) = 2

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

\int \frac{9 x ^{2} + 5 x + 9}{( x ^{2} + 1 ) ^{2}} d x