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Popular >

derivative of z/(1+z^2)

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d z}{d z} = 1

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

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

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

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

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Frequently Asked Questions (FAQ)

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