What is the derivative of (2x+1/x) ?

The derivative of (2x+1/x) is -1/(x^2)

What is the first derivative of (2x+1/x) ?

The first derivative of (2x+1/x) is -1/(x^2)

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\frac{d}{d x} (\frac{2 x + 1}{x})

- \frac{1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 1}{x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{1}{x ^{2}}

f (x) = \frac{( x + 1 )}{x - 1}

\frac{\partial}{\partial y} (x + 1)

\frac{d}{d x} (e^{g (x)} cos (x))

f (x) = - 2 x sin (x^{2})

x \to - \infty lim (- 2 x^{3})

What is the derivative of (2x+1/x) ?
The derivative of (2x+1/x) is -1/(x^2)
What is the first derivative of (2x+1/x) ?
The first derivative of (2x+1/x) is -1/(x^2)