Question

Tentukan turunan dari
[tex]\rm f(x)=\frac{x^5+2x^2-7x}{x-1}[/tex]​

Answer 1

Jawaban:

turunan fungsi aljabar

[tex]f(x) = {ax}^{n} \to \: f'(x) = n. {ax}^{n - 1} \\ [/tex]

[tex]f(x) = \frac{ {x}^{5} + 2 {x}^{2} - 7x}{x - 1} \\ [/tex]

misalkan:

[tex]u = {x}^{5} + 2 {x}^{2} - 7x \\ u' = 5 {x}^{4} + 4x - 7 \\ v = x - 1 \\ v' = 1[/tex]

[tex]f'(x) = \frac{ u'v - v'u}{ {v}^{2} } \\ f'(x) = \frac{(5 {x}^{4} + 4x - 7)(x - 1) - 1( {x}^{5} + 2 {x}^{2} - 7x) }{(x - 1) {}^{2} } \\ f'(x) = \frac{5 {x}^{5} + 4 {x}^{2} - 7x - 5 {x}^{4} - 4x + 7 - {x}^{5} - 2 {x}^{2} + 7x }{ {x}^{2} - 2x + 1 } \\ f'(x) = \frac{4 {x}^{5} - 5 {x}^{4} + 2 {x}^{2} - 4x + 7 }{ {x}^{2} - 2x + 1} [/tex]