What is the derivative of y= 9/(sqrt(x+8)) ?

The derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}

What is the first derivative of y= 9/(sqrt(x+8)) ?

The first derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = \frac{9}{x + 8}

- \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{9}{x + 8})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{1}{x + 8})

Apply exponent rule:

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

= 9 \frac{d}{d x} ((x + 8)^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

= - \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= 9 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1)

Simplify

9 (- \frac{1}{2 ( x + 8 ) ^{\frac{3}{2}}} \cdot 1) : - \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

= - \frac{9}{2 ( x + 8 ) ^{\frac{3}{2}}}

x \to π lim (\frac{( cos ( x ) + 1 )}{( x - π ) ^{2}})

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

2 - 7 x

\int \frac{1}{x ^{2}} - \frac{3}{x ^{4}} d x

2 t e^{3 t} + 4 t^{2} e^{- 5 t}

What is the derivative of y= 9/(sqrt(x+8)) ?
The derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}
What is the first derivative of y= 9/(sqrt(x+8)) ?
The first derivative of y= 9/(sqrt(x+8)) is -9/(2(x+8)^{3/2)}