What is the derivative of (5ln(4x))/(2-3x) ?

The derivative of (5ln(4x))/(2-3x) is (5(2-3x+3xln(4x)))/(x(2-3x)^2)

What is the first derivative of (5ln(4x))/(2-3x) ?

The first derivative of (5ln(4x))/(2-3x) is (5(2-3x+3xln(4x)))/(x(2-3x)^2)

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derivative of

\frac{5 ln ( 4 x )}{2 - 3 x}

\frac{5 ( 2 - 3 x + 3 x ln ( 4 x ) )}{x ( 2 - 3 x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{5 ln ( 4 x )}{2 - 3 x})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{ln ( 4 x )}{2 - 3 x})

Apply the Quotient Rule:

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

= 5 \cdot \frac{\frac{d}{d x} ( ln ( 4 x ) ) ( 2 - 3 x ) - \frac{d}{d x} ( 2 - 3 x ) ln ( 4 x )}{( 2 - 3 x ) ^{2}}

\frac{d}{d x} (ln (4 x)) = \frac{1}{x}

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

= 5 \cdot \frac{\frac{1}{x} ( 2 - 3 x ) - ( - 3 ) ln ( 4 x )}{( 2 - 3 x ) ^{2}}

Simplify

5 \cdot \frac{\frac{1}{x} ( 2 - 3 x ) - ( - 3 ) ln ( 4 x )}{( 2 - 3 x ) ^{2}} : \frac{5 ( 2 - 3 x + 3 x ln ( 4 x ) )}{x ( 2 - 3 x ) ^{2}}

= \frac{5 ( 2 - 3 x + 3 x ln ( 4 x ) )}{x ( 2 - 3 x ) ^{2}}

What is the derivative of (5ln(4x))/(2-3x) ?
The derivative of (5ln(4x))/(2-3x) is (5(2-3x+3xln(4x)))/(x(2-3x)^2)
What is the first derivative of (5ln(4x))/(2-3x) ?
The first derivative of (5ln(4x))/(2-3x) is (5(2-3x+3xln(4x)))/(x(2-3x)^2)