What is the derivative of kaln((x+d/(x-d))) ?

The derivative of kaln((x+d/(x-d))) is -(2akd)/((x+d)(x-d))

What is the first derivative of kaln((x+d/(x-d))) ?

The first derivative of kaln((x+d/(x-d))) is -(2akd)/((x+d)(x-d))

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

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

Solution steps

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

Treat

a, k, d

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

ka \frac{1}{\frac{x + d}{x - d}} (- \frac{2 d}{( x - d ) ^{2}}) : - \frac{2 ak d}{( x + d ) ( x - d )}

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

\frac{1}{2} cos (7 x)

\frac{d y}{d x} = y^{2} + 2 y

\frac{d}{d x} (arccot (5 x^{2}))

\frac{\partial}{\partial x} (e^{i x})

y^{^{'}} + y = t

What is the derivative of kaln((x+d/(x-d))) ?
The derivative of kaln((x+d/(x-d))) is -(2akd)/((x+d)(x-d))
What is the first derivative of kaln((x+d/(x-d))) ?
The first derivative of kaln((x+d/(x-d))) is -(2akd)/((x+d)(x-d))