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

The derivative of y/(y+a/y) is (2ay)/((y^2+a)^2)

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

The first derivative of y/(y+a/y) is (2ay)/((y^2+a)^2)

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derivative of

\frac{y}{y + \frac{a}{y}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d y}{d y} = 1

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

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

Simplify

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

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

n = 0 \sum \infty \frac{n}{e ^{2 n}}

\int \frac{e ^{4 x} - e ^{2 x} + 1}{e ^{x}} d x

y^{^{'}} = y

f (x) = 4 x - 6

tan (sec (cos (t)))

What is the derivative of y/(y+a/y) ?
The derivative of y/(y+a/y) is (2ay)/((y^2+a)^2)
What is the first derivative of y/(y+a/y) ?
The first derivative of y/(y+a/y) is (2ay)/((y^2+a)^2)