What is the derivative of (3x+2)/(4x) ?

The derivative of (3x+2)/(4x) is -1/(2x^2)

What is the first derivative of (3x+2)/(4x) ?

The first derivative of (3x+2)/(4x) is -1/(2x^2)

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derivative of

\frac{3 x + 2}{4 x}

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

Solution steps

\frac{d}{d x} (\frac{3 x + 2}{4 x})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{3 x + 2}{x})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 3 x + 2 ) x - \frac{d x}{d x} ( 3 x + 2 )}{x ^{2}}

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

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

= \frac{1}{4} \cdot \frac{3 x - 1 \cdot ( 3 x + 2 )}{x ^{2}}

Simplify

\frac{1}{4} \cdot \frac{3 x - 1 \cdot ( 3 x + 2 )}{x ^{2}} : - \frac{1}{2 x ^{2}}

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

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What is the derivative of (3x+2)/(4x) ?
The derivative of (3x+2)/(4x) is -1/(2x^2)
What is the first derivative of (3x+2)/(4x) ?
The first derivative of (3x+2)/(4x) is -1/(2x^2)