What is the derivative of (x^2^{1/2}) ?

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

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

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

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

\frac{1}{2 x}

Solution steps

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

Apply the Power Rule:

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

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

Simplify

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

= \frac{1}{2 x}

\frac{d}{d x} (\frac{2 x + 3}{x + 2})

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

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

\int \frac{1}{t + 2} d t

\int_{- 1}^{2} x^{2} e^{x^{3} + 1} d x

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