What is the derivative of log_{e}((3+x/(3-x))) ?

The derivative of log_{e}((3+x/(3-x))) is 6/((x+3)(-x+3))

What is the first derivative of log_{e}((3+x/(3-x))) ?

The first derivative of log_{e}((3+x/(3-x))) is 6/((x+3)(-x+3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (lo g_{e} (\frac{3 + x}{3 - x}))

\frac{6}{( x + 3 ) ( - x + 3 )}

Solution steps

\frac{d}{d x} (lo g_{e} (\frac{3 + x}{3 - x}))

Simplify

lo g_{e} (\frac{3 + x}{3 - x}) : ln (\frac{3 + x}{3 - x})

= \frac{d}{d x} (ln (\frac{3 + x}{3 - x}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{3 + x}{3 - x}) = \frac{6}{( 3 - x ) ^{2}}

= \frac{1}{\frac{3 + x}{3 - x}} \cdot \frac{6}{( 3 - x ) ^{2}}

Simplify

\frac{1}{\frac{3 + x}{3 - x}} \cdot \frac{6}{( 3 - x ) ^{2}} : \frac{6}{( x + 3 ) ( - x + 3 )}

= \frac{6}{( x + 3 ) ( - x + 3 )}

\frac{d}{d x} (\frac{8 x}{x ^{2} + 1})

\int 8 e^{- k x} d x

\int \frac{1}{x ^{2} + 6 x + 16} d x

x \to 0 lim (\frac{sin ( x )}{9 x})

6 x^{2} y^{^{''}} + 13 x y^{^{'}} + y = 70 x + 2

What is the derivative of log_{e}((3+x/(3-x))) ?
The derivative of log_{e}((3+x/(3-x))) is 6/((x+3)(-x+3))
What is the first derivative of log_{e}((3+x/(3-x))) ?
The first derivative of log_{e}((3+x/(3-x))) is 6/((x+3)(-x+3))