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

The derivative of x/(x+d/x) is (2dx)/((x^2+d)^2)

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

The first derivative of x/(x+d/x) is (2dx)/((x^2+d)^2)

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derivative of

\frac{x}{x + \frac{d}{x}}

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

Solution steps

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

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

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

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

Simplify

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

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

f (x) = (2 x^{5} - 3)^{8}

x \to + (- 2.4) lim (x)

y^{^{'}} - t y^{3} = 0

n = 7 \sum \infty \frac{1}{n}

x \to - 5 lim (\frac{x - 1}{x + 5})

What is the derivative of x/(x+d/x) ?
The derivative of x/(x+d/x) is (2dx)/((x^2+d)^2)
What is the first derivative of x/(x+d/x) ?
The first derivative of x/(x+d/x) is (2dx)/((x^2+d)^2)