What is the derivative of ln(sqrt((9-x/(5+x)))) ?

The derivative of ln(sqrt((9-x/(5+x)))) is -7/((x+5)(-x+9))

What is the first derivative of ln(sqrt((9-x/(5+x)))) ?

The first derivative of ln(sqrt((9-x/(5+x)))) is -7/((x+5)(-x+9))

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\frac{d}{d x} (ln (\frac{9 - x}{5 + x}))

- \frac{7}{( x + 5 ) ( - x + 9 )}

Solution steps

\frac{d}{d x} (ln (\frac{9 - x}{5 + x}))

Apply the chain rule:

\frac{1}{\frac{9 - x}{5 + x}} \frac{d}{d x} (\frac{9 - x}{5 + x})

= \frac{1}{\frac{9 - x}{5 + x}} \frac{d}{d x} (\frac{9 - x}{5 + x})

\frac{d}{d x} (\frac{9 - x}{5 + x}) = - \frac{7}{- x + 9 ( x + 5 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{9 - x}{5 + x}} (- \frac{7}{- x + 9 ( x + 5 ) ^{\frac{3}{2}}})

Simplify

\frac{1}{\frac{9 - x}{5 + x}} (- \frac{7}{- x + 9 ( x + 5 ) ^{\frac{3}{2}}}) : - \frac{7}{( x + 5 ) ( - x + 9 )}

= - \frac{7}{( x + 5 ) ( - x + 9 )}

- 9 x^{2}

\frac{d}{d x} (arccos (cos (x)))

\frac{d y}{d x}, x y = x - 2 y

\frac{d y}{d x} = \frac{( x - 3 )}{y - 4}

\int \frac{289}{x ^{3} - 17 x ^{2}} d x

What is the derivative of ln(sqrt((9-x/(5+x)))) ?
The derivative of ln(sqrt((9-x/(5+x)))) is -7/((x+5)(-x+9))
What is the first derivative of ln(sqrt((9-x/(5+x)))) ?
The first derivative of ln(sqrt((9-x/(5+x)))) is -7/((x+5)(-x+9))