What is the derivative of 1/(sqrt(x+8)) ?

The derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}

What is the first derivative of 1/(sqrt(x+8)) ?

The first derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{1}{x + 8}

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

Solution steps

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

Apply exponent rule:

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

= \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

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

Simplify

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

d er i v a t i v e f (x) = 9 sin (3 x)

\int_{0}^{5} 3 f (x) d x

\int x^{3} 1 + x^{2} d x

\frac{d}{d x} (2 A x)

y^{^{'}} = 2 y - 3 y^{2}

What is the derivative of 1/(sqrt(x+8)) ?
The derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}
What is the first derivative of 1/(sqrt(x+8)) ?
The first derivative of 1/(sqrt(x+8)) is -1/(2(x+8)^{3/2)}