What is the derivative of (sqrt(x)+3/(sqrt(x)-5)) ?

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

What is the first derivative of (sqrt(x)+3/(sqrt(x)-5)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{x + 3}{x - 5})

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

Solution steps

\frac{d}{d x} (\frac{x + 3}{x - 5})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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