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

The derivative of (\sqrt[3]{x})/4 is 1/(12x^{2/3)}

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

The first derivative of (\sqrt[3]{x})/4 is 1/(12x^{2/3)}

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derivative of

\frac{3 x}{4}

\frac{1}{12 x ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (\frac{3 x}{4})

Take the constant out:

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

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

Apply radical rule:

n a = a^{\frac{1}{n}}

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{4} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{12 x ^{\frac{2}{3}}}

= \frac{1}{12 x ^{\frac{2}{3}}}

\int \frac{1}{25 x ^{2} - 49} d x

\int \frac{6 - x}{4 x ^{2} - 12 x + 7} d x

t y^{^{'}} + 3 y = t^{2} - t + 7

x \to 0 lim (\frac{1}{x})

x \to 2 lim (x^{3} - 4 x)

What is the derivative of (\sqrt[3]{x})/4 ?
The derivative of (\sqrt[3]{x})/4 is 1/(12x^{2/3)}
What is the first derivative of (\sqrt[3]{x})/4 ?
The first derivative of (\sqrt[3]{x})/4 is 1/(12x^{2/3)}