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

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

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

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

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

Solution steps

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

Apply radical rule:

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

Apply the Power Rule:

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

= 4 \cdot \frac{1}{4} x^{\frac{1}{4} - 1}

Simplify

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

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

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