What is the derivative of (x+1/(x^{2/3)(x+3)^{1/3}}) ?

The derivative of (x+1/(x^{2/3)(x+3)^{1/3}}) is -2/(x^{5/3)(x+3)^{4/3}}

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

The first derivative of (x+1/(x^{2/3)(x+3)^{1/3}}) is -2/(x^{5/3)(x+3)^{4/3}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- \frac{2}{x ^{\frac{5}{3}} ( x + 3 ) ^{\frac{4}{3}}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (x + 1) = 1

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

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

Simplify

\frac{1 \cdot x ^{\frac{2}{3}} ( x + 3 ) ^{\frac{1}{3}} - \frac{x + 2}{x ^{\frac{1}{3}} ( x + 3 ) ^{\frac{2}{3}}} ( x + 1 )}{( x ^{\frac{2}{3}} ( x + 3 ) ^{\frac{1}{3}} ) ^{2}} : - \frac{2}{x ^{\frac{5}{3}} ( x + 3 ) ^{\frac{4}{3}}}

= - \frac{2}{x ^{\frac{5}{3}} ( x + 3 ) ^{\frac{4}{3}}}

\int e^{k x} d x

\int t - \frac{1}{t} d t

(1, 5), (- 2, - 4)

x y^{^{'}} + y = 8 x y^{2}, y (1) = 5

\int_{0}^{\frac{π}{2}} 9 sin^{2} (2 x) d x

What is the derivative of (x+1/(x^{2/3)(x+3)^{1/3}}) ?
The derivative of (x+1/(x^{2/3)(x+3)^{1/3}}) is -2/(x^{5/3)(x+3)^{4/3}}
What is the first derivative of (x+1/(x^{2/3)(x+3)^{1/3}}) ?
The first derivative of (x+1/(x^{2/3)(x+3)^{1/3}}) is -2/(x^{5/3)(x+3)^{4/3}}