What is the derivative of sin(x^{1/3}) ?

The derivative of sin(x^{1/3}) is (cos(x^{1/3}))/(3x^{2/3)}

What is the first derivative of sin(x^{1/3}) ?

The first derivative of sin(x^{1/3}) is (cos(x^{1/3}))/(3x^{2/3)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative

\frac{cos ( x ^{\frac{1}{3}} )}{3 x ^{\frac{2}{3}}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of sin(x^{1/3}) ?
The derivative of sin(x^{1/3}) is (cos(x^{1/3}))/(3x^{2/3)}
What is the first derivative of sin(x^{1/3}) ?
The first derivative of sin(x^{1/3}) is (cos(x^{1/3}))/(3x^{2/3)}