en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x/(sqrt(x-7))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of (2x-1)/(4x^2-1)

\int \frac{2 x - 1}{4 x ^{2} - 1} d x

integral from 0 to 4 of pi(4y^2-(y^4)/4)

\int_{0}^{4} π (4 y^{2} - \frac{y ^{4}}{4}) d y

derivative of-4t(6t^4-1)^7 derivative of

- 4 t (6 t^{4} - 1)^{7}

integral from 0 to 1 of x^2(1+2x^3)^5

\int_{0}^{1} x^{2} (1 + 2 x^{3})^{5} d x

derivative of y=(4x^2+6x+4)/(sqrt(x))derivative of

y = \frac{4 x ^{2} + 6 x + 4}{x}

Frequently Asked Questions (FAQ)

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