What is the derivative of (sqrt(x)/(\sqrt[3]{2x)}) ?

The derivative of (sqrt(x)/(\sqrt[3]{2x)}) is 1/(6\sqrt[3]{2)\sqrt[6]{x}x^{2/3}}

What is the first derivative of (sqrt(x)/(\sqrt[3]{2x)}) ?

The first derivative of (sqrt(x)/(\sqrt[3]{2x)}) is 1/(6\sqrt[3]{2)\sqrt[6]{x}x^{2/3}}

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Solution steps

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

Simplify

What is the derivative of (sqrt(x)/(\sqrt[3]{2x)}) ?
The derivative of (sqrt(x)/(\sqrt[3]{2x)}) is 1/(6\sqrt[3]{2)\sqrt[6]{x}x^{2/3}}
What is the first derivative of (sqrt(x)/(\sqrt[3]{2x)}) ?
The first derivative of (sqrt(x)/(\sqrt[3]{2x)}) is 1/(6\sqrt[3]{2)\sqrt[6]{x}x^{2/3}}