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

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

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

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

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derivative of

\frac{3 x}{2 ( 1 - 2 x )}

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

Solution steps

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

Take the constant out:

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

= \frac{3}{2} \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}}

= \frac{3}{2} \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

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

Simplify

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

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

\int cos (\frac{θ}{2}) d θ

\frac{d}{d x} (x^{2} sin (x) + 2 x cos (x) - 2 sin (x))

\int_{9}^{16} \frac{1}{9 - x} d x

\frac{d}{d x} (- \frac{11}{( x - 3 ) ^{2}})

\frac{\partial}{\partial x} (x y e^{- x - y})

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