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

The derivative of ln((5-x/(5+x))) is -(10)/((-x+5)(x+5))

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

The first derivative of ln((5-x/(5+x))) is -(10)/((-x+5)(x+5))

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

- \frac{10}{( - x + 5 ) ( x + 5 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{5 - x}{5 + x}) = - \frac{10}{( 5 + x ) ^{2}}

= \frac{1}{\frac{5 - x}{5 + x}} (- \frac{10}{( 5 + x ) ^{2}})

Simplify

\frac{1}{\frac{5 - x}{5 + x}} (- \frac{10}{( 5 + x ) ^{2}}) : - \frac{10}{( - x + 5 ) ( x + 5 )}

= - \frac{10}{( - x + 5 ) ( x + 5 )}

\int x^{2} (11 + x^{3}) d x

\int_{5}^{6} 12 arccot (x) d x

(- 5, 3), (5, - 5)

\frac{d}{d x} (x cos (θ))

What is the derivative of ln((5-x/(5+x))) ?
The derivative of ln((5-x/(5+x))) is -(10)/((-x+5)(x+5))
What is the first derivative of ln((5-x/(5+x))) ?
The first derivative of ln((5-x/(5+x))) is -(10)/((-x+5)(x+5))