What is the derivative of 1/(z^2+1) ?

The derivative of 1/(z^2+1) is -(2z)/((z^2+1)^2)

What is the first derivative of 1/(z^2+1) ?

The first derivative of 1/(z^2+1) is -(2z)/((z^2+1)^2)

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derivative of

\frac{1}{z ^{2} + 1}

- \frac{2 z}{( z ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d z} (\frac{1}{z ^{2} + 1})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d z} (z^{2} + 1) = 2 z

= - \frac{1}{( z ^{2} + 1 ) ^{2}} \cdot 2 z

Simplify

- \frac{1}{( z ^{2} + 1 ) ^{2}} \cdot 2 z : - \frac{2 z}{( z ^{2} + 1 ) ^{2}}

= - \frac{2 z}{( z ^{2} + 1 ) ^{2}}

x^{- 5} (1 + x^{- 1}), at x = 1

y = x^{2}, y^{2} = x

f (x) = 5 x - x^{2}

y^{^{''}} - 10 y + 2 y = 0

x^{^{'}} + 3 x = 0

What is the derivative of 1/(z^2+1) ?
The derivative of 1/(z^2+1) is -(2z)/((z^2+1)^2)
What is the first derivative of 1/(z^2+1) ?
The first derivative of 1/(z^2+1) is -(2z)/((z^2+1)^2)