What is the derivative of (x+3/(2x+1)) ?

The derivative of (x+3/(2x+1)) is -5/((2x+1)^2)

What is the first derivative of (x+3/(2x+1)) ?

The first derivative of (x+3/(2x+1)) is -5/((2x+1)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( 2 x + 1 ) - 2 ( x + 3 )}{( 2 x + 1 ) ^{2}} : - \frac{5}{( 2 x + 1 ) ^{2}}

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

What is the derivative of (x+3/(2x+1)) ?
The derivative of (x+3/(2x+1)) is -5/((2x+1)^2)
What is the first derivative of (x+3/(2x+1)) ?
The first derivative of (x+3/(2x+1)) is -5/((2x+1)^2)