What is the derivative of ((11ln(x)))/((2x+4)) ?

The derivative of ((11ln(x)))/((2x+4)) is (11(x+2-xln(x)))/(2x(x+2)^2)

What is the first derivative of ((11ln(x)))/((2x+4)) ?

The first derivative of ((11ln(x)))/((2x+4)) is (11(x+2-xln(x)))/(2x(x+2)^2)

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derivative of

\frac{( 11 ln ( x ) )}{( 2 x + 4 )}

\frac{11 ( x + 2 - x ln ( x ) )}{2 x ( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{11 ln ( x )}{2 x + 4})

Take the constant out:

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

= 11 \frac{d}{d x} (\frac{ln ( x )}{2 x + 4})

Apply the Quotient Rule:

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

= 11 \cdot \frac{\frac{d}{d x} ( ln ( x ) ) ( 2 x + 4 ) - \frac{d}{d x} ( 2 x + 4 ) ln ( x )}{( 2 x + 4 ) ^{2}}

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

\frac{d}{d x} (2 x + 4) = 2

= 11 \cdot \frac{\frac{1}{x} ( 2 x + 4 ) - 2 ln ( x )}{( 2 x + 4 ) ^{2}}

Simplify

11 \cdot \frac{\frac{1}{x} ( 2 x + 4 ) - 2 ln ( x )}{( 2 x + 4 ) ^{2}} : \frac{11 ( x + 2 - x ln ( x ) )}{2 x ( x + 2 ) ^{2}}

= \frac{11 ( x + 2 - x ln ( x ) )}{2 x ( x + 2 ) ^{2}}

What is the derivative of ((11ln(x)))/((2x+4)) ?
The derivative of ((11ln(x)))/((2x+4)) is (11(x+2-xln(x)))/(2x(x+2)^2)
What is the first derivative of ((11ln(x)))/((2x+4)) ?
The first derivative of ((11ln(x)))/((2x+4)) is (11(x+2-xln(x)))/(2x(x+2)^2)