What is the derivative of 6(x+2)^{1/2} ?

The derivative of 6(x+2)^{1/2} is 3/((x+2)^{1/2)}

What is the first derivative of 6(x+2)^{1/2} ?

The first derivative of 6(x+2)^{1/2} is 3/((x+2)^{1/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

6 (x + 2)^{\frac{1}{2}}

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

Solution steps

\frac{d}{d x} (6 (x + 2)^{\frac{1}{2}})

Take the constant out:

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

= 6 \frac{d}{d x} ((x + 2)^{\frac{1}{2}})

Apply the chain rule:

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

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

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

= 6 \cdot \frac{1}{2 ( x + 2 ) ^{\frac{1}{2}}} \cdot 1

Simplify

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

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

What is the derivative of 6(x+2)^{1/2} ?
The derivative of 6(x+2)^{1/2} is 3/((x+2)^{1/2)}
What is the first derivative of 6(x+2)^{1/2} ?
The first derivative of 6(x+2)^{1/2} is 3/((x+2)^{1/2)}