What is the derivative of sqrt(\sqrt{x)} ?

The derivative of sqrt(\sqrt{x)} is 1/(4x^{3/4)}

What is the first derivative of sqrt(\sqrt{x)} ?

The first derivative of sqrt(\sqrt{x)} is 1/(4x^{3/4)}

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Popular >

\frac{d}{d x} (x)

\frac{1}{4 x ^{\frac{3}{4}}}

Solution steps

\frac{d}{d x} (x)

Apply radical rule:

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

Apply the Power Rule:

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

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

Simplify

\frac{\frac{1}{2}}{2} x^{\frac{\frac{1}{2}}{2} - 1} : \frac{1}{4 x ^{\frac{3}{4}}}

= \frac{1}{4 x ^{\frac{3}{4}}}

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What is the derivative of sqrt(\sqrt{x)} ?
The derivative of sqrt(\sqrt{x)} is 1/(4x^{3/4)}
What is the first derivative of sqrt(\sqrt{x)} ?
The first derivative of sqrt(\sqrt{x)} is 1/(4x^{3/4)}