Penjelasan dengan langkah-langkah:
Turunan fungsi aljabar
[tex]p(x) = ax {}^{n} \to \: p'(x) = n \: . \: {ax}^{n - 1} \\ [/tex]
maka:
[tex]f(x) = \frac{3}{ \sqrt{(3x {}^{2} + 7) {}^{3} } } \\ f(x) = 3 \: . \: (3 {x}^{2} + 7) {}^{ - \frac{3}{2} } \\ f'(x) = 3 \: . \: ( - \frac{3}{2} )(3 {x}^{2} + 7) {}^{ - \frac{3}{2} - 1} \: . \: 6x \\ f'(x) = - \frac{9}{2} \: . \: 6x(3 {x}^{2} + 7) {}^{ - \frac{5}{2} } \\ f'(x) = - 9 \: . \: 3x(3 {x}^{2} + 7) {}^{ - \frac{5}{2} } \\ f'(x) = - 27x \: (3 {x}^{2} + 7) {}^{ - \frac{5}{2} } \\ f'(x) = - \frac{27x}{(3 {x}^{2} + 7) {}^{ \frac{5}{2} } } \\ f'(x) = - \frac{27x}{ \sqrt{(3 {x}^{2} + 7) {}^{5} } } [/tex]
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Penjelasan dengan langkah-langkah:
Turunan fungsi aljabar
[tex]p(x) = ax {}^{n} \to \: p'(x) = n \: . \: {ax}^{n - 1} \\ [/tex]
maka:
[tex]f(x) = \frac{3}{ \sqrt{(3x {}^{2} + 7) {}^{3} } } \\ f(x) = 3 \: . \: (3 {x}^{2} + 7) {}^{ - \frac{3}{2} } \\ f'(x) = 3 \: . \: ( - \frac{3}{2} )(3 {x}^{2} + 7) {}^{ - \frac{3}{2} - 1} \: . \: 6x \\ f'(x) = - \frac{9}{2} \: . \: 6x(3 {x}^{2} + 7) {}^{ - \frac{5}{2} } \\ f'(x) = - 9 \: . \: 3x(3 {x}^{2} + 7) {}^{ - \frac{5}{2} } \\ f'(x) = - 27x \: (3 {x}^{2} + 7) {}^{ - \frac{5}{2} } \\ f'(x) = - \frac{27x}{(3 {x}^{2} + 7) {}^{ \frac{5}{2} } } \\ f'(x) = - \frac{27x}{ \sqrt{(3 {x}^{2} + 7) {}^{5} } } [/tex]