en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x+9)/(sqrt(x))

Solution

derivative of

\frac{x + 9}{x}

Solution

\frac{x - 9}{2 x x}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x - 9}{2 x x}

Popular Examples

d/(dt)(e^{-t}sin(2t))

\frac{d}{d t} (e^{- t} sin (2 t))

slope ofintercept (-4,0),(1,-5)slope intercept

(- 4, 0), (1, - 5)

tangent of f(x)= 1/2 x^2,\at x=-1 tangent of

f (x) = \frac{1}{2} x^{2}, at x = - 1

laplacetransform 4e^{3t}laplace transform

4 e^{3 t}

integral of sin(pi/2 x)

\int sin (\frac{π}{2} x) d x

Frequently Asked Questions (FAQ)

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