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Popular >

derivative of ln(((4-x))/(4+x))

Solution

derivative of

ln (\frac{( 4 - x )}{4 + x})

Solution

- \frac{8}{( - x + 4 ) ( x + 4 )}

Solution steps

\frac{d}{d x} (ln (\frac{4 - x}{4 + x}))

Apply the chain rule:

\frac{1}{\frac{4 - x}{4 + x}} \frac{d}{d x} (\frac{4 - x}{4 + x})

= \frac{1}{\frac{4 - x}{4 + x}} \frac{d}{d x} (\frac{4 - x}{4 + x})

\frac{d}{d x} (\frac{4 - x}{4 + x}) = - \frac{8}{( 4 + x ) ^{2}}

= \frac{1}{\frac{4 - x}{4 + x}} (- \frac{8}{( 4 + x ) ^{2}})

Simplify

\frac{1}{\frac{4 - x}{4 + x}} (- \frac{8}{( 4 + x ) ^{2}}) : - \frac{8}{( - x + 4 ) ( x + 4 )}

= - \frac{8}{( - x + 4 ) ( x + 4 )}

Popular Examples

integral of 2/(x+1)

\int \frac{2}{x + 1} d x

y^'=(xy^2-0.5sin(2x))/(y(1-x^2)),y(0)=2

y^{^{'}} = \frac{x y ^{2} - 0.5 sin ( 2 x )}{y ( 1 - x ^{2} )}, y (0) = 2

y^'=(t+y)^2-1,y(2)=6

y^{^{'}} = (t + y)^{2} - 1, y (2) = 6

derivative of ((x+2/(x-2))^5)

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

derivative of 2x^2+y^2

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(((4-x))/(4+x)) ?
The derivative of ln(((4-x))/(4+x)) is -8/((-x+4)(x+4))
What is the first derivative of ln(((4-x))/(4+x)) ?
The first derivative of ln(((4-x))/(4+x)) is -8/((-x+4)(x+4))