What is the derivative of \sqrt[4]{x^3} ?

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

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