What is the derivative of f(x)= x/(7-sqrt(x)) ?

The derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^2)

What is the first derivative of f(x)= x/(7-sqrt(x)) ?

The first derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^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}{7 - x}

\frac{14 - x}{2 ( 7 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{7 - x})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 7 - x ) - \frac{d}{d x} ( 7 - x ) x}{( 7 - x ) ^{2}}

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

\frac{d}{d x} (7 - x) = - \frac{1}{2 x}

= \frac{1 \cdot ( 7 - x ) - ( - \frac{1}{2 x} ) x}{( 7 - x ) ^{2}}

Simplify

\frac{1 \cdot ( 7 - x ) - ( - \frac{1}{2 x} ) x}{( 7 - x ) ^{2}} : \frac{14 - x}{2 ( 7 - x ) ^{2}}

= \frac{14 - x}{2 ( 7 - x ) ^{2}}

h \to 0 lim (5 h^{2} + 8 h - 12)

\int_{- 5}^{2} (x^{2} + 3 x - 10) d x

\frac{1}{s ^{2} + 4 s + 5}

\int \frac{1}{1 + t ^{2}} d t

- sec (x) + 2 sec^{3} (x)

What is the derivative of f(x)= x/(7-sqrt(x)) ?
The derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^2)
What is the first derivative of f(x)= x/(7-sqrt(x)) ?
The first derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^2)