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

The derivative of x/(x+b/x) is (2bx)/((x^2+b)^2)

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

The first derivative of x/(x+b/x) is (2bx)/((x^2+b)^2)

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

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

Solution steps

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

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

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

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

Simplify

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

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

x \to 3 + lim (a^{2} x - 12 a)

(2 x - 1) d x + (5 y + 4) d y = 0

y = x^{3}, y = 0, x = - 3, x = 3

\frac{1}{( s + 2 ) ^{2} + 9}

\frac{\partial}{\partial x} (2 x - 3 y + 5)

What is the derivative of x/(x+b/x) ?
The derivative of x/(x+b/x) is (2bx)/((x^2+b)^2)
What is the first derivative of x/(x+b/x) ?
The first derivative of x/(x+b/x) is (2bx)/((x^2+b)^2)