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Popular >

derivative of ln((2-x/(2+x)))

Solution

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

Solution

- \frac{4}{( - x + 2 ) ( x + 2 )}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (arctan^4(x))/(1+x^2)

\int \frac{arctan ^{4} ( x )}{1 + x ^{2}} d x

limit as x approaches 0 of ln((1/x)^x)

x \to 0 lim (ln ((\frac{1}{x})^{x}))

integral of ((ln(x))/(sqrt(x^3)))

\int (\frac{ln ( x )}{x ^{3}}) d x

derivative of (10/((x-2)^3))

\frac{d}{d x} (\frac{10}{( x - 2 ) ^{3}})

(\partial)/(\partial y)(sqrt(4x^2+6xy+y^2))

\frac{\partial}{\partial y} (4 x^{2} + 6 x y + y^{2})

Frequently Asked Questions (FAQ)

What is the derivative of ln((2-x/(2+x))) ?
The derivative of ln((2-x/(2+x))) is -4/((-x+2)(x+2))
What is the first derivative of ln((2-x/(2+x))) ?
The first derivative of ln((2-x/(2+x))) is -4/((-x+2)(x+2))