What is the derivative of xx^{1/2} ?

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

What is the first derivative of xx^{1/2} ?

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

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

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

Solution steps

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

Simplify

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

= \frac{d}{d x} (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}

5 x^{2} + x y + 5 y^{2} = 11, (1, 1)

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\frac{d}{d x} (sin^{5} (x^{2} + 1)^{7})

\int 3 x^{2} e^{4 x} d x

\int \frac{( x + 1 )}{x x - 2} d x

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