What is the derivative of (4x/((2x+1)^2)) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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