What is the derivative of 1/(y^n-1) ?

The derivative of 1/(y^n-1) is -(ny^{n-1})/((y^n-1)^2)

What is the first derivative of 1/(y^n-1) ?

The first derivative of 1/(y^n-1) is -(ny^{n-1})/((y^n-1)^2)

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derivative of

\frac{1}{y ^{n} - 1}

- \frac{n y ^{n - 1}}{( y ^{n} - 1 ) ^{2}}

Solution steps

\frac{d}{d y} (\frac{1}{y ^{n} - 1})

Apply exponent rule:

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

= \frac{d}{d y} ((y^{n} - 1)^{- 1})

Apply the chain rule:

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

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

\frac{d}{d y} (y^{n} - 1) = n y^{n - 1}

= - \frac{1}{( y ^{n} - 1 ) ^{2}} n y^{n - 1}

Simplify

- \frac{1}{( y ^{n} - 1 ) ^{2}} n y^{n - 1} : - \frac{n y ^{n - 1}}{( y ^{n} - 1 ) ^{2}}

= - \frac{n y ^{n - 1}}{( y ^{n} - 1 ) ^{2}}

What is the derivative of 1/(y^n-1) ?
The derivative of 1/(y^n-1) is -(ny^{n-1})/((y^n-1)^2)
What is the first derivative of 1/(y^n-1) ?
The first derivative of 1/(y^n-1) is -(ny^{n-1})/((y^n-1)^2)