Turunan kedua dari f(x)= (1 - x)/(1 + x) adalah

[tex]f(x) = \frac{1 - x}{1 + x} [/tex]

cari turunan pertama
u = 1 - x u' = -1
v = 1 + x. v' = 1

[tex] {f}^{l} = \frac{u. {v}^{l} - {u}^{l}.v }{ {v}^{2} } [/tex]

[tex] {f}^{l} = \frac{1(1 - x) - ( - 1)(1 + x)}{ {(1 + x)}^{2} } \\ {f}^{l} = \frac{1 - x + 1 + x}{ {(1 + x)}^{2} } \\ {f}^{l} = \frac{2}{ {(1 + x)}^{2} } [/tex]

untuk turunan ke dua
u = 2 u" = 0
v = (1 + x)² = x² + 2x + 1
v" = 2x + 2

[tex] {f}^{ll} = \frac{2(2x +2) - (0)( {x}^{2} + 2x + 1)} { {( {(1 + x)}^{2}) }^{2} } \\ {f}^{ll} = \frac{4x + 4}{ {(1 + x)}^{4} } [/tex]
atau
[tex] {f}^{ll} = \frac{4x + 4}{( {x}^{4} + 4 {x}^{3} + {6x}^{2} + 4x + 1) } [/tex]