What is the derivative of 1/(sqrt(b-mt)) ?

The derivative of 1/(sqrt(b-mt)) is -1/(2(b-mt)^{3/2)}

What is the first derivative of 1/(sqrt(b-mt)) ?

The first derivative of 1/(sqrt(b-mt)) is -1/(2(b-mt)^{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}{b - m t}

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

Solution steps

\frac{d}{d b} (\frac{1}{b - m t})

Treat

m, t

as constants

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d b} (b - m t) = 1

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

Simplify

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

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