What is the derivative of y= 1/2 \sqrt[3]{x} ?

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

What is the first derivative of y= 1/2 \sqrt[3]{x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{1}{6 x ^{\frac{2}{3}}}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

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

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

Simplify

\frac{1}{2} \cdot \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{1}{6 x ^{\frac{2}{3}}}

= \frac{1}{6 x ^{\frac{2}{3}}}

2 y^{^{''}} + y^{^{'}} + y = 0

t^{2} (5 t + 9)^{3}

2 x^{3} - 3 x^{2}

\frac{1}{x - 1}, 0

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

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