What is the derivative of (2x+3/(2x)) ?

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

What is the first derivative of (2x+3/(2x)) ?

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

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\frac{d}{d x} (\frac{2 x + 3}{2 x})

- \frac{3}{2 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 3}{2 x})

Take the constant out:

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

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

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

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

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

Simplify

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

= - \frac{3}{2 x ^{2}}

\frac{d}{d x} (\frac{x}{sin ( x )})

\frac{\partial ^{2}}{\partial y ^{2}} (sin^{2} (m x + n y))

\int \frac{x ^{2}}{4 x ^{2} + 9} d x

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

3 x^{2}, x^{3}

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