What is the derivative of ln(sqrt((9-x^2/(9+x^2)))) ?

The derivative of ln(sqrt((9-x^2/(9+x^2)))) is -(18x)/((x^2+9)(-x^2+9))

What is the first derivative of ln(sqrt((9-x^2/(9+x^2)))) ?

The first derivative of ln(sqrt((9-x^2/(9+x^2)))) is -(18x)/((x^2+9)(-x^2+9))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (ln (\frac{9 - x ^{2}}{9 + x ^{2}}))

- \frac{18 x}{( x ^{2} + 9 ) ( - x ^{2} + 9 )}

Solution steps

\frac{d}{d x} (ln (\frac{9 - x ^{2}}{9 + x ^{2}}))

Apply the chain rule:

\frac{1}{\frac{9 - x ^{2}}{9 + x ^{2}}} \frac{d}{d x} (\frac{9 - x ^{2}}{9 + x ^{2}})

= \frac{1}{\frac{9 - x ^{2}}{9 + x ^{2}}} \frac{d}{d x} (\frac{9 - x ^{2}}{9 + x ^{2}})

\frac{d}{d x} (\frac{9 - x ^{2}}{9 + x ^{2}}) = - \frac{18 x}{- x ^{2} + 9 ( x ^{2} + 9 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{9 - x ^{2}}{9 + x ^{2}}} (- \frac{18 x}{- x ^{2} + 9 ( x ^{2} + 9 ) ^{\frac{3}{2}}})

Simplify

\frac{1}{\frac{9 - x ^{2}}{9 + x ^{2}}} (- \frac{18 x}{- x ^{2} + 9 ( x ^{2} + 9 ) ^{\frac{3}{2}}}) : - \frac{18 x}{( x ^{2} + 9 ) ( - x ^{2} + 9 )}

= - \frac{18 x}{( x ^{2} + 9 ) ( - x ^{2} + 9 )}

y^{^{'}} = x y - 3 y

x \to 8 lim (x^{\frac{2}{3}})

\frac{d ^{2}}{d y ^{2}} (ln (x^{2} + y^{2}))

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

y^{^{''}} + y^{^{'}} - 2 y = e^{- x}

What is the derivative of ln(sqrt((9-x^2/(9+x^2)))) ?
The derivative of ln(sqrt((9-x^2/(9+x^2)))) is -(18x)/((x^2+9)(-x^2+9))
What is the first derivative of ln(sqrt((9-x^2/(9+x^2)))) ?
The first derivative of ln(sqrt((9-x^2/(9+x^2)))) is -(18x)/((x^2+9)(-x^2+9))