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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Simplify

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

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

x^{2} - 2 x, - x^{2} + 4 x

\int \frac{2}{x + 2} d x

f (x) = 2 x + 1 + \frac{6}{x}, at x = 2

sin (4 x)

x \to 0 + lim (\frac{2}{x ^{2} - x})

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