What is the derivative of \sqrt[3]{(x^2+2^2}) ?

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution steps

Apply the chain rule:

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

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

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

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

Simplify

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

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

5 t^{\frac{7}{5}} + 5 e^{3}

y^{^{'}} = 7 y^{2} sin (x)

\frac{d}{d m} (5 m^{2} + 15 m^{3})

\int \frac{x}{x ^{2} + a ^{2}} d x

\int 34 x + 20 \cdot (- \frac{1}{10}) x + 1 d x

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