What is the derivative of x/(x+c/x) ?

The derivative of x/(x+c/x) is (2cx)/((x^2+c)^2)

What is the first derivative of x/(x+c/x) ?

The first derivative of x/(x+c/x) is (2cx)/((x^2+c)^2)

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derivative of

\frac{x}{x + \frac{c}{x}}

\frac{2 c x}{( x ^{2} + c ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{x + \frac{c}{x}})

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

= \frac{2 c x}{( x ^{2} + c ) ^{2}}

f (x) = e^{x} - 6 x^{5}

5 sin (7 t)

y^{^{'''}} - 3 y^{^{''}} - 4 y^{^{'}} = 0

f (t) = 106 - 80 e^{- 0.4 t}

\int 3^{x} d x

What is the derivative of x/(x+c/x) ?
The derivative of x/(x+c/x) is (2cx)/((x^2+c)^2)
What is the first derivative of x/(x+c/x) ?
The first derivative of x/(x+c/x) is (2cx)/((x^2+c)^2)