What is the derivative of sqrt((4-x^{2/3)^3}) ?

The derivative of sqrt((4-x^{2/3)^3}) is -((4-x^{2/3})^{1/2})/(x^{1/3)}

What is the first derivative of sqrt((4-x^{2/3)^3}) ?

The first derivative of sqrt((4-x^{2/3)^3}) is -((4-x^{2/3})^{1/2})/(x^{1/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to - 8 lim (1 + - 2 x)

\frac{\partial}{\partial x} (x - 2)

\int y sin (x + y^{2}) d y

y^{^{'}} = 3 y t

\int_{0}^{5} f (x) d x

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