What is the derivative of (ax+b/(ax-b)) ?

The derivative of (ax+b/(ax-b)) is -(2ab)/((ax-b)^2)

What is the first derivative of (ax+b/(ax-b)) ?

The first derivative of (ax+b/(ax-b)) is -(2ab)/((ax-b)^2)

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\frac{d}{d x} (\frac{a x + b}{a x - b})

- \frac{2 ab}{( a x - b ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{a x + b}{a x - b})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (a x + b) = a

\frac{d}{d x} (a x - b) = a

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

Simplify

\frac{a ( a x - b ) - a ( a x + b )}{( a x - b ) ^{2}} : - \frac{2 ab}{( a x - b ) ^{2}}

= - \frac{2 ab}{( a x - b ) ^{2}}

f (x) = x^{2} + 4, (3, 13)

\int e^{- x} d x

\frac{\partial}{\partial x} (ln (2))

32 - 2 x^{2}, [0, 7]

x \to 0 lim (\frac{( x ^{3} )}{tan ^{3} ( 2 x )})

What is the derivative of (ax+b/(ax-b)) ?
The derivative of (ax+b/(ax-b)) is -(2ab)/((ax-b)^2)
What is the first derivative of (ax+b/(ax-b)) ?
The first derivative of (ax+b/(ax-b)) is -(2ab)/((ax-b)^2)