What is the derivative of x/(8x+3) ?

The derivative of x/(8x+3) is 3/((8x+3)^2)

What is the first derivative of x/(8x+3) ?

The first derivative of x/(8x+3) is 3/((8x+3)^2)

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\frac{d}{d x} (\frac{x}{8 x + 3})

\frac{3}{( 8 x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{8 x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 8 x + 3 ) - \frac{d}{d x} ( 8 x + 3 ) x}{( 8 x + 3 ) ^{2}}

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

\frac{d}{d x} (8 x + 3) = 8

= \frac{1 \cdot ( 8 x + 3 ) - 8 x}{( 8 x + 3 ) ^{2}}

Simplify

= \frac{3}{( 8 x + 3 ) ^{2}}

What is the derivative of x/(8x+3) ?
The derivative of x/(8x+3) is 3/((8x+3)^2)
What is the first derivative of x/(8x+3) ?
The first derivative of x/(8x+3) is 3/((8x+3)^2)