What is the derivative of (sqrt(x)-8)/(sqrt(x)+8) ?

The derivative of (sqrt(x)-8)/(sqrt(x)+8) is 8/(sqrt(x)(\sqrt{x)+8)^2}

What is the first derivative of (sqrt(x)-8)/(sqrt(x)+8) ?

The first derivative of (sqrt(x)-8)/(sqrt(x)+8) is 8/(sqrt(x)(\sqrt{x)+8)^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x - 8}{x + 8}

\frac{8}{x ( x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x - 8}{x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 8 ) ( x + 8 ) - \frac{d}{d x} ( x + 8 ) ( x - 8 )}{( x + 8 ) ^{2}}

\frac{d}{d x} (x - 8) = \frac{1}{2 x}

\frac{d}{d x} (x + 8) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 8 ) - \frac{1}{2 x} ( x - 8 )}{( x + 8 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 8 ) - \frac{1}{2 x} ( x - 8 )}{( x + 8 ) ^{2}} : \frac{8}{x ( x + 8 ) ^{2}}

= \frac{8}{x ( x + 8 ) ^{2}}

e^{x} + 1, at x = 0

\int (3 + 2 x)^{- 3} d x

\int 2 x^{3} ln (x^{2}) d x

y = 3 + 2 x, y = \frac{9 + x}{3}

\frac{d}{d x} (a^{f (x) (x^{2})})

What is the derivative of (sqrt(x)-8)/(sqrt(x)+8) ?
The derivative of (sqrt(x)-8)/(sqrt(x)+8) is 8/(sqrt(x)(\sqrt{x)+8)^2}
What is the first derivative of (sqrt(x)-8)/(sqrt(x)+8) ?
The first derivative of (sqrt(x)-8)/(sqrt(x)+8) is 8/(sqrt(x)(\sqrt{x)+8)^2}