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