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

The derivative of sqrt(x\sqrt{x)} is 3/(4\sqrt[4]{x)}

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

The first derivative of sqrt(x\sqrt{x)} is 3/(4\sqrt[4]{x)}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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