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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int (cos (x) + \frac{1}{4} x) d x

\int sin^{23} (x) d x

x \to - 4 + lim (5 x + 20 - 8)

n = 0 \sum \infty - 1^{n}

\int \frac{2 x + 1}{x ^{2} + 2 x + 122} d x

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