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

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

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

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

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derivative of

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = - 3 x^{3} - 2 x, (- 1, 5)

x^{2} y^{^{'}} + y = 0

n lo g_{10} (n)

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

\int 9 x^{2} sin (8 x) d x

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