What is the derivative of (24x/(2x+3)) ?

The derivative of (24x/(2x+3)) is (72)/((2x+3)^2)

What is the first derivative of (24x/(2x+3)) ?

The first derivative of (24x/(2x+3)) is (72)/((2x+3)^2)

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\frac{d}{d x} (\frac{24 x}{2 x + 3})

\frac{72}{( 2 x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{24 x}{2 x + 3})

Take the constant out:

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

= 24 \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}}

= 24 \cdot \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

= 24 \cdot \frac{1 \cdot ( 2 x + 3 ) - 2 x}{( 2 x + 3 ) ^{2}}

Simplify

24 \cdot \frac{1 \cdot ( 2 x + 3 ) - 2 x}{( 2 x + 3 ) ^{2}} : \frac{72}{( 2 x + 3 ) ^{2}}

= \frac{72}{( 2 x + 3 ) ^{2}}

x \to 0 lim (\frac{x}{- x})

t^{\frac{3}{2}}

\int (x^{2} + \frac{1}{4} y^{2} + 3) d x

\frac{d y}{d t} = 0.03 y + 3600

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

What is the derivative of (24x/(2x+3)) ?
The derivative of (24x/(2x+3)) is (72)/((2x+3)^2)
What is the first derivative of (24x/(2x+3)) ?
The first derivative of (24x/(2x+3)) is (72)/((2x+3)^2)