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)}

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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}}}

n = 5 \sum \infty cos (\frac{1}{n ^{3}})

\frac{x ^{2}}{x ^{2} - 1}

\frac{99 x ^{\frac{7}{2}}}{4}

\int \frac{2 x + 6}{( ( x + 1 ) ^{2} + 9 ) ^{4}} d x

f (x) = \frac{375}{x ^{4}}

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)}