What is the derivative of f(x)= 7/(sqrt(x-6)) ?

The derivative of f(x)= 7/(sqrt(x-6)) is -7/(2(x-6)^{3/2)}

What is the first derivative of f(x)= 7/(sqrt(x-6)) ?

The first derivative of f(x)= 7/(sqrt(x-6)) is -7/(2(x-6)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = \frac{7}{x - 6}

- \frac{7}{2 ( x - 6 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{7}{x - 6})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (\frac{1}{x - 6})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 7 \frac{d}{d x} ((x - 6)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x - 6 ) ^{\frac{3}{2}}} \frac{d}{d x} (x - 6)

= - \frac{1}{2 ( x - 6 ) ^{\frac{3}{2}}} \frac{d}{d x} (x - 6)

\frac{d}{d x} (x - 6) = 1

= 7 (- \frac{1}{2 ( x - 6 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

7 (- \frac{1}{2 ( x - 6 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{7}{2 ( x - 6 ) ^{\frac{3}{2}}}

= - \frac{7}{2 ( x - 6 ) ^{\frac{3}{2}}}

What is the derivative of f(x)= 7/(sqrt(x-6)) ?
The derivative of f(x)= 7/(sqrt(x-6)) is -7/(2(x-6)^{3/2)}
What is the first derivative of f(x)= 7/(sqrt(x-6)) ?
The first derivative of f(x)= 7/(sqrt(x-6)) is -7/(2(x-6)^{3/2)}