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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

\int_{1}^{1 - 2 y} \frac{y}{x} d x

\frac{d}{d x} (9 x^{2} + y^{2})

y = 5 x^{2}, (4, 80)

x \to - \infty lim (- ln (x))

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

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