What is the derivative of x/(5x+2) ?

The derivative of x/(5x+2) is 2/((5x+2)^2)

What is the first derivative of x/(5x+2) ?

The first derivative of x/(5x+2) is 2/((5x+2)^2)

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derivative of

\frac{x}{5 x + 2}

\frac{2}{( 5 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{5 x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 5 x + 2 ) - \frac{d}{d x} ( 5 x + 2 ) x}{( 5 x + 2 ) ^{2}}

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

\frac{d}{d x} (5 x + 2) = 5

= \frac{1 \cdot ( 5 x + 2 ) - 5 x}{( 5 x + 2 ) ^{2}}

Simplify

= \frac{2}{( 5 x + 2 ) ^{2}}

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What is the derivative of x/(5x+2) ?
The derivative of x/(5x+2) is 2/((5x+2)^2)
What is the first derivative of x/(5x+2) ?
The first derivative of x/(5x+2) is 2/((5x+2)^2)