What is the derivative of 2/(sqrt(x+3)) ?

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

What is the first derivative of 2/(sqrt(x+3)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{2}{x + 3}

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

Solution steps

\frac{d}{d x} (\frac{2}{x + 3})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

18 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

\frac{\partial}{\partial w} (u v - w)

\int e^{3 l n (x)} d x

12 x e^{- x}

n = 1 \sum \infty \frac{n}{2 n + 5}

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