What is the derivative of (3x)/(x-3/x) ?

The derivative of (3x)/(x-3/x) is -(18x)/((x^2-3)^2)

What is the first derivative of (3x)/(x-3/x) ?

The first derivative of (3x)/(x-3/x) is -(18x)/((x^2-3)^2)

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derivative of

\frac{3 x}{x - \frac{3}{x}}

- \frac{18 x}{( x ^{2} - 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{x - \frac{3}{x}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{x}{x - \frac{3}{x}})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d x}{d x} ( x - \frac{3}{x} ) - \frac{d}{d x} ( x - \frac{3}{x} ) x}{( x - \frac{3}{x} ) ^{2}}

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

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

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

Simplify

3 \cdot \frac{1 \cdot ( x - \frac{3}{x} ) - ( 1 + \frac{3}{x ^{2}} ) x}{( x - \frac{3}{x} ) ^{2}} : - \frac{18 x}{( x ^{2} - 3 ) ^{2}}

= - \frac{18 x}{( x ^{2} - 3 ) ^{2}}

\frac{35}{4 + x + x}

\frac{d}{d x} (\frac{x - 6}{x + 4})

x \to \infty lim (4 (x - 3))

x \to \infty lim (x (0))

y^{2} - 2 x = 7, y - x = 4

What is the derivative of (3x)/(x-3/x) ?
The derivative of (3x)/(x-3/x) is -(18x)/((x^2-3)^2)
What is the first derivative of (3x)/(x-3/x) ?
The first derivative of (3x)/(x-3/x) is -(18x)/((x^2-3)^2)