What is the derivative of (x^2-2sqrt(x)/x) ?

The derivative of (x^2-2sqrt(x)/x) is (x^2+sqrt(x))/(x^2)

What is the first derivative of (x^2-2sqrt(x)/x) ?

The first derivative of (x^2-2sqrt(x)/x) is (x^2+sqrt(x))/(x^2)

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

\frac{x ^{2} + x}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x ^{2} + x}{x ^{2}}

What is the derivative of (x^2-2sqrt(x)/x) ?
The derivative of (x^2-2sqrt(x)/x) is (x^2+sqrt(x))/(x^2)
What is the first derivative of (x^2-2sqrt(x)/x) ?
The first derivative of (x^2-2sqrt(x)/x) is (x^2+sqrt(x))/(x^2)