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

The derivative of z/(z+d/z) is (2zd)/((z^2+d)^2)

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

The first derivative of z/(z+d/z) is (2zd)/((z^2+d)^2)

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derivative of

\frac{z}{z + \frac{d}{z}}

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

Solution steps

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

Treat

d

as a constant

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

ln (4 x)

\frac{\partial}{\partial y} (2 x - 2 x y)

f^{^{'}} (x) = x^{\frac{1}{3}} (2 x - 1) (x + 1)

f (x) = 2 x + 1, at x = \frac{1}{4}

\int 4 e^{\frac{x}{2}} d x

What is the derivative of z/(z+d/z) ?
The derivative of z/(z+d/z) is (2zd)/((z^2+d)^2)
What is the first derivative of z/(z+d/z) ?
The first derivative of z/(z+d/z) is (2zd)/((z^2+d)^2)