What is the derivative of z/(z+a/z) ?

The derivative of z/(z+a/z) is (2az)/((z^2+a)^2)

What is the first derivative of z/(z+a/z) ?

The first derivative of z/(z+a/z) is (2az)/((z^2+a)^2)

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derivative of

\frac{z}{z + \frac{a}{z}}

\frac{2 a z}{( z ^{2} + a ) ^{2}}

Solution steps

\frac{d}{d z} (\frac{z}{z + \frac{a}{z}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{2 a z}{( z ^{2} + a ) ^{2}}

\int_{0}^{x^{2} + 3} \frac{1}{x ^{2} + 3} d x

y = 2 x^{3} + 3 x^{2} - 12 x + 3

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

(u - u) (u + u)

y^{^{'}} + 2 y = e^{- x}

What is the derivative of z/(z+a/z) ?
The derivative of z/(z+a/z) is (2az)/((z^2+a)^2)
What is the first derivative of z/(z+a/z) ?
The first derivative of z/(z+a/z) is (2az)/((z^2+a)^2)