What is the derivative of ln(((1-x)/((x+5)^3))) ?

The derivative of ln(((1-x)/((x+5)^3))) is -(2(-x+4))/((-x+1)(x+5))

What is the first derivative of ln(((1-x)/((x+5)^3))) ?

The first derivative of ln(((1-x)/((x+5)^3))) is -(2(-x+4))/((-x+1)(x+5))

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\frac{d}{d x} (ln (\frac{( 1 - x )}{( x + 5 ) ^{3}}))

- \frac{2 ( - x + 4 )}{( - x + 1 ) ( x + 5 )}

Solution steps

\frac{d}{d x} (ln (\frac{( 1 - x )}{( x + 5 ) ^{3}}))

Apply the chain rule:

\frac{1}{\frac{1 - x}{( x + 5 ) ^{3}}} \frac{d}{d x} (\frac{1 - x}{( x + 5 ) ^{3}})

= \frac{1}{\frac{1 - x}{( x + 5 ) ^{3}}} \frac{d}{d x} (\frac{1 - x}{( x + 5 ) ^{3}})

\frac{d}{d x} (\frac{1 - x}{( x + 5 ) ^{3}}) = - \frac{2 ( - x + 4 )}{( x + 5 ) ^{4}}

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

Simplify

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

= - \frac{2 ( - x + 4 )}{( - x + 1 ) ( x + 5 )}

What is the derivative of ln(((1-x)/((x+5)^3))) ?
The derivative of ln(((1-x)/((x+5)^3))) is -(2(-x+4))/((-x+1)(x+5))
What is the first derivative of ln(((1-x)/((x+5)^3))) ?
The first derivative of ln(((1-x)/((x+5)^3))) is -(2(-x+4))/((-x+1)(x+5))