What is the derivative of (x-sqrt(x)/(x^{1/6)}) ?

The derivative of (x-sqrt(x)/(x^{1/6)}) is (sqrt(x)-1)/(3x^{2/3)}+1/(2x^{1/6)}

What is the first derivative of (x-sqrt(x)/(x^{1/6)}) ?

The first derivative of (x-sqrt(x)/(x^{1/6)}) is (sqrt(x)-1)/(3x^{2/3)}+1/(2x^{1/6)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{x - x}{x ^{\frac{1}{6}}})

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

Solution steps

\frac{d}{d x} (\frac{x - x}{x ^{\frac{1}{6}}})

Simplify

\frac{x - x}{x ^{\frac{1}{6}}} : x^{\frac{1}{3}} (x - 1)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{1}{3}}, g = x - 1

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

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

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

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

Simplify

\frac{1}{3 x ^{\frac{2}{3}}} (x - 1) + \frac{1}{2 x ^{\frac{1}{2}}} x^{\frac{1}{3}} : \frac{x - 1}{3 x ^{\frac{2}{3}}} + \frac{1}{2 x ^{\frac{1}{6}}}

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

\frac{d x}{d t} = e^{x} sin (t)

e^{2 s i n (3 v)}

2 - 2 x

f (x) = \frac{x - ln ( 1 + x )}{x ^{2}}

\int 63 sec^{4} (θ) tan^{6} (θ) d θ

What is the derivative of (x-sqrt(x)/(x^{1/6)}) ?
The derivative of (x-sqrt(x)/(x^{1/6)}) is (sqrt(x)-1)/(3x^{2/3)}+1/(2x^{1/6)}
What is the first derivative of (x-sqrt(x)/(x^{1/6)}) ?
The first derivative of (x-sqrt(x)/(x^{1/6)}) is (sqrt(x)-1)/(3x^{2/3)}+1/(2x^{1/6)}