What is the derivative of (4x/(x-5)) ?

The derivative of (4x/(x-5)) is -(20)/((x-5)^2)

What is the first derivative of (4x/(x-5)) ?

The first derivative of (4x/(x-5)) is -(20)/((x-5)^2)

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{4 x}{x - 5})

- \frac{20}{( x - 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x}{x - 5})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (\frac{x}{x - 5})

Apply the Quotient Rule:

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

= 4 \cdot \frac{\frac{d x}{d x} ( x - 5 ) - \frac{d}{d x} ( x - 5 ) x}{( x - 5 ) ^{2}}

\frac{d x}{d x} = 1

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

= 4 \cdot \frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}}

Simplify

4 \cdot \frac{1 \cdot ( x - 5 ) - 1 \cdot x}{( x - 5 ) ^{2}} : - \frac{20}{( x - 5 ) ^{2}}

= - \frac{20}{( x - 5 ) ^{2}}

y^{^{'}} - x y = x y^{\frac{3}{2}}

\frac{1}{x}

y = 9 arctan (x - 1 + x^{2})

\int \frac{x}{x - 5} d x

\int arctan (y) d y

What is the derivative of (4x/(x-5)) ?
The derivative of (4x/(x-5)) is -(20)/((x-5)^2)
What is the first derivative of (4x/(x-5)) ?
The first derivative of (4x/(x-5)) is -(20)/((x-5)^2)