What is the derivative of 1/(in(x-1)) ?

The derivative of 1/(in(x-1)) is i 1/(n+nx^2-2nx)

What is the first derivative of 1/(in(x-1)) ?

The first derivative of 1/(in(x-1)) is i 1/(n+nx^2-2nx)

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\frac{d}{d x} (\frac{1}{in ( x - 1 )})

i \frac{1}{n + n x ^{2} - 2 n x}

Solution steps

\frac{d}{d x} (\frac{1}{in ( x - 1 )})

Simplify

\frac{1}{in ( x - 1 )} : - i \frac{1}{- n + n x}

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= i \frac{1}{n + n x ^{2} - 2 n x}

What is the derivative of 1/(in(x-1)) ?
The derivative of 1/(in(x-1)) is i 1/(n+nx^2-2nx)
What is the first derivative of 1/(in(x-1)) ?
The first derivative of 1/(in(x-1)) is i 1/(n+nx^2-2nx)