What is the derivative of (3x^{3/5}-x)/(x-1) ?

The derivative of (3x^{3/5}-x)/(x-1) is (-6x-9+5x^{2/5})/(5x^{2/5)(x-1)^2}

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

The first derivative of (3x^{3/5}-x)/(x-1) is (-6x-9+5x^{2/5})/(5x^{2/5)(x-1)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{3 x ^{\frac{3}{5}} - x}{x - 1}

\frac{- 6 x - 9 + 5 x ^{\frac{2}{5}}}{5 x ^{\frac{2}{5}} ( x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{\frac{3}{5}} - x}{x - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x ^{\frac{3}{5}} - x ) ( x - 1 ) - \frac{d}{d x} ( x - 1 ) ( 3 x ^{\frac{3}{5}} - x )}{( x - 1 ) ^{2}}

\frac{d}{d x} (3 x^{\frac{3}{5}} - x) = \frac{9}{5 x ^{\frac{2}{5}}} - 1

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

= \frac{( \frac{9}{5 x ^{\frac{2}{5}}} - 1 ) ( x - 1 ) - 1 \cdot ( 3 x ^{\frac{3}{5}} - x )}{( x - 1 ) ^{2}}

Simplify

\frac{( \frac{9}{5 x ^{\frac{2}{5}}} - 1 ) ( x - 1 ) - 1 \cdot ( 3 x ^{\frac{3}{5}} - x )}{( x - 1 ) ^{2}} : \frac{- 6 x - 9 + 5 x ^{\frac{2}{5}}}{5 x ^{\frac{2}{5}} ( x - 1 ) ^{2}}

= \frac{- 6 x - 9 + 5 x ^{\frac{2}{5}}}{5 x ^{\frac{2}{5}} ( x - 1 ) ^{2}}

\int \frac{x + 1}{x ^{2} + 2 x + 5} d x

\int - 5 x^{4} d x

\int csc^{2} (x) - 2 e^{x} d x

\int_{0}^{\frac{1}{4}} \frac{1}{1 + 16 x ^{2}} d x

\frac{d y}{d t} = y^{2} t^{2}

What is the derivative of (3x^{3/5}-x)/(x-1) ?
The derivative of (3x^{3/5}-x)/(x-1) is (-6x-9+5x^{2/5})/(5x^{2/5)(x-1)^2}
What is the first derivative of (3x^{3/5}-x)/(x-1) ?
The first derivative of (3x^{3/5}-x)/(x-1) is (-6x-9+5x^{2/5})/(5x^{2/5)(x-1)^2}