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Popular >

derivative of ln((3-x/(3+x)))

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Popular Examples

d/(dt)(0.5t^2e^{-0.6t})

\frac{d}{d t} (0.5 t^{2} e^{- 0.6 t})

integral from-1 to 5 of |x-3x^2|

\int_{- 1}^{5} x - 3 x^{2} d x

integral of (log_{2}(u))/u

\int \frac{lo g _{2} ( u )}{u} d x

derivative of x/(1-sin(x))

\frac{d}{d x} (\frac{x}{1 - sin ( x )})

inverse oflaplace 1/(s(2s^2+2s+1))inverse laplace

\frac{1}{s ( 2 s ^{2} + 2 s + 1 )}

Frequently Asked Questions (FAQ)

What is the derivative of ln((3-x/(3+x))) ?
The derivative of ln((3-x/(3+x))) is -6/((-x+3)(x+3))
What is the first derivative of ln((3-x/(3+x))) ?
The first derivative of ln((3-x/(3+x))) is -6/((-x+3)(x+3))