What is the derivative of 9/(sqrt(x+2)) ?

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

What is the first derivative of 9/(sqrt(x+2)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{9}{x + 2}

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

Solution steps

\frac{d}{d x} (\frac{9}{x + 2})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + 2) = 1

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

Simplify

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

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

\frac{\partial}{\partial x} (x y e^{z} + x - z^{2} - 3)

\int sin^{3} (10 x) d x

t an g e n t y = x^{2} - x + 4, at x = 4

x \to - 0 lim (\frac{1}{1 + e ^{\frac{1}{x}}})

x \to - 6 lim (x - 10)

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