What is the derivative of 5/(sqrt(x+9)) ?

The derivative of 5/(sqrt(x+9)) is -5/(2(x+9)^{3/2)}

What is the first derivative of 5/(sqrt(x+9)) ?

The first derivative of 5/(sqrt(x+9)) is -5/(2(x+9)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{5}{x + 9}

- \frac{5}{2 ( x + 9 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{5}{x + 9})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{x + 9})

Apply exponent rule:

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

= 5 \frac{d}{d x} ((x + 9)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 9)

= - \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 9)

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

= 5 (- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

5 (- \frac{1}{2 ( x + 9 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{5}{2 ( x + 9 ) ^{\frac{3}{2}}}

= - \frac{5}{2 ( x + 9 ) ^{\frac{3}{2}}}

What is the derivative of 5/(sqrt(x+9)) ?
The derivative of 5/(sqrt(x+9)) is -5/(2(x+9)^{3/2)}
What is the first derivative of 5/(sqrt(x+9)) ?
The first derivative of 5/(sqrt(x+9)) is -5/(2(x+9)^{3/2)}