What is the derivative of x/(sqrt(x)+9) ?

The derivative of x/(sqrt(x)+9) is (sqrt(x)+18)/(2(sqrt(x)+9)^2)

What is the first derivative of x/(sqrt(x)+9) ?

The first derivative of x/(sqrt(x)+9) is (sqrt(x)+18)/(2(sqrt(x)+9)^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}{x + 9}

\frac{x + 18}{2 ( x + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( x + 9 ) - \frac{d}{d x} ( x + 9 ) x}{( x + 9 ) ^{2}}

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

\frac{d}{d x} (x + 9) = \frac{1}{2 x}

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

Simplify

\frac{1 \cdot ( x + 9 ) - \frac{1}{2 x} x}{( x + 9 ) ^{2}} : \frac{x + 18}{2 ( x + 9 ) ^{2}}

= \frac{x + 18}{2 ( x + 9 ) ^{2}}

y = e^{- 4 t}, at t = 0

\frac{1 + csc ( x ^{7} )}{1 - cot ( x ^{7} )}

\int \frac{x - 1}{x} d x

\int cosh (2 ln (x)) d x

\int \frac{sin ( θ )}{cos ^{2} ( θ )} d θ

What is the derivative of x/(sqrt(x)+9) ?
The derivative of x/(sqrt(x)+9) is (sqrt(x)+18)/(2(sqrt(x)+9)^2)
What is the first derivative of x/(sqrt(x)+9) ?
The first derivative of x/(sqrt(x)+9) is (sqrt(x)+18)/(2(sqrt(x)+9)^2)