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

The derivative of f(x)=(sqrt(x))/(x+8) is (-x+8)/(2sqrt(x)(x+8)^2)

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

The first derivative of f(x)=(sqrt(x))/(x+8) is (-x+8)/(2sqrt(x)(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

f (x) = \frac{x}{x + 8}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int tan^{\frac{3}{2}} (x) sec^{4} (x) d x

\int \frac{3 x + 16}{x ^{2} - x - 6} d x

x \to 1 lim (0.8 x + 1.2)

x \to 0 lim (cos (x) sin (x))

What is the derivative of f(x)=(sqrt(x))/(x+8) ?
The derivative of f(x)=(sqrt(x))/(x+8) is (-x+8)/(2sqrt(x)(x+8)^2)
What is the first derivative of f(x)=(sqrt(x))/(x+8) ?
The first derivative of f(x)=(sqrt(x))/(x+8) is (-x+8)/(2sqrt(x)(x+8)^2)