What is the derivative of sqrt((Inx+1/(Inx-1))) ?

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

What is the first derivative of sqrt((Inx+1/(Inx-1))) ?

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

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\frac{d}{d x} (\frac{I n x + 1}{I n x - 1})

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

Solution steps

\frac{d}{d x} (\frac{I n x + 1}{I n x - 1})

Treat

n, I

as a constant

Apply the chain rule:

\frac{1}{2 \frac{I n x + 1}{I n x - 1}} \frac{d}{d x} (\frac{I n x + 1}{I n x - 1})

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

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

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

Simplify

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

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

\int_{0}^{1} \frac{1}{2} e^{- 2 x} d x

\int_{- 2}^{2} \frac{1}{2} (16 - x^{4}) d x

\int cos (3 x + 4) d x

\int \frac{x + ln ( x )}{x} d x

\frac{d}{d x} (\frac{a}{x ^{b}})

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