Matematika

Pertanyaan

F(x)= x'2-2x akar 2
F''(x)= ....

1 Jawaban


  • [tex]F(x) = {( {x}^{2} -2x)}^{ \frac{1}{2} } \\
    F'(x) = (2x-2) \times \frac{1}{2} \times {( {x}^{2} -2x)}^{ - \frac{1}{2} } \\ F'(x) = (x-1) \times {( {x}^{2} -2x)}^{ - \frac{1}{2} } \\ U = (x-1) \\U' = 1\\ V = {( {x}^{2} -2x)}^{ - \frac{1}{2} }\\ V' = - \frac{2x - 2}{2 {( {x}^{2} -2x)}^{ \frac{3}{2} } } = \frac{1 - x}{ {( {x}^{2} -2x)}^{ \frac{3}{2} } } \\ \\ F''(x) = U' \times V + V' \times U \\ F''(x) =1 \times {( {x}^{2} -2x)}^{ - \frac{1}{2} } + \frac{1 - x}{ {( {x}^{2} -2x)}^{ \frac{3}{2} } } \times (x-1) \\ F''(x) = \frac{{( {x}^{2} -2x)}^{ \frac{3}{2} } + ( - {x}^{2} + 2x - 1) \times {( {x}^{2} -2x)}^{ \frac{1}{2} } }{{( {x}^{2} -2x)}^{ \frac{3}{2} } \times{( {x}^{2} -2x)}^{ \frac{1}{2} } } [/tex]


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