What is the derivative of 1/2 (2t+1)^{-1/2} ?

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

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

The first derivative of 1/2 (2t+1)^{-1/2} is -1/(2(2t+1)^{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{1}{2} (2 t + 1)^{- \frac{1}{2}}

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

a x^{2} e^{2 x}

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

n = 1 \sum \infty \frac{6}{n ^{2} + 2 n}

\int_{1}^{10} \frac{21}{x ^{3}} d x

x \to - 1 lim (\frac{4}{( x + 1 ) ^{2}})

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