What is the derivative of \sqrt[4]{x^2} ?

The derivative of \sqrt[4]{x^2} is 1/(2x^{1/2)}

What is the first derivative of \sqrt[4]{x^2} ?

The first derivative of \sqrt[4]{x^2} is 1/(2x^{1/2)}

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

Solution steps

Apply the chain rule:

\frac{1}{4 ( x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{2})

= \frac{1}{4 ( x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{2})

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

= \frac{1}{4 ( x ^{2} ) ^{\frac{3}{4}}} \cdot 2 x

Simplify

\frac{1}{4 ( x ^{2} ) ^{\frac{3}{4}}} \cdot 2 x : \frac{1}{2 x ^{\frac{1}{2}}}

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

\int - 9 csc^{2} (x) d x

g (x) = 11 x

g (x) = 9 - x^{2}

\frac{\partial}{\partial y} (5 x y e^{x z})

f (x) = - 4 - x^{2}

What is the derivative of \sqrt[4]{x^2} ?
The derivative of \sqrt[4]{x^2} is 1/(2x^{1/2)}
What is the first derivative of \sqrt[4]{x^2} ?
The first derivative of \sqrt[4]{x^2} is 1/(2x^{1/2)}