4. - Universityku

$f(x) frac{(x ^{2} + 1) ^{3} }{(x - 2)^{5} }$
cari turunan pertama…
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4.

Penjelasan dengan langkah-langkah:

misal

$u = ( {x}^{2} + 1) ^{3} \ u' = 3( {x}^{2} + 1) ^{2} (2x) = 6x( {x}^{2} + 1) ^{2}$

$v = (x - 2) ^{5} \ v '= 5(x - 2) ^{4}$

f'(x)= (u'v-uv')/v^2

$= frac{6x( {x}^{2} + 1) ^{2} (x-2)^{5} - ( {x}^{2} + 1) ^{3} (5(x - 2) ^{4} )}{(x - 2) ^{5(2)} }$

$= frac{6x( {x}^{2} + 1) ^{2}(x-2)^{5} - ( {x}^{2} + 1) ^{3} (5(x - 2) ^{4} )}{(x - 2) ^{10} }$

$= frac{6x(x-2)( {x}^{2} + 1) ^{2} }{(x - 2) ^{6} } - frac{5( {x}^{2} + 1) ^{3} }{(x - 2) ^{6} }$

$= frac{({x}^{2}+1)^{2}(x^2-12x-5)}{(x-2)^{6}}$