Jikamaka f'(-1) ?Turunan pecahanmakamaka
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![\sf f(x)=\frac{4x-1}{5x-2} \sf f(x)=\frac{4x-1}{5x-2}](https://tex.z-dn.net/?f=%5Csf%20f%28x%29%3D%5Cfrac%7B4x-1%7D%7B5x-2%7D)
![\sf(\frac{u}{v})'=\frac{u'\cdot v - v'\cdot u}{v^2} \sf(\frac{u}{v})'=\frac{u'\cdot v - v'\cdot u}{v^2}](https://tex.z-dn.net/?f=%5Csf%28%5Cfrac%7Bu%7D%7Bv%7D%29%27%3D%5Cfrac%7Bu%27%5Ccdot%20v%20-%20v%27%5Ccdot%20u%7D%7Bv%5E2%7D)
![\sf(\frac{4x-1}{5x-2})'=\\\\\frac{(4x-1)'(5x-2) - (5x-2)'(4x-1)}{(5x-2)^2}=\\\\\frac{4(5x-2) - 5(4x-1)}{(5x-2)(5x-2)}=\\\\\frac{20x-8-20x+5}{25x^2-2(2)(5x)+2^2}=\\\\\displaystyle -\frac{3}{25x^2-20x+4} \sf(\frac{4x-1}{5x-2})'=\\\\\frac{(4x-1)'(5x-2) - (5x-2)'(4x-1)}{(5x-2)^2}=\\\\\frac{4(5x-2) - 5(4x-1)}{(5x-2)(5x-2)}=\\\\\frac{20x-8-20x+5}{25x^2-2(2)(5x)+2^2}=\\\\\displaystyle -\frac{3}{25x^2-20x+4}](https://tex.z-dn.net/?f=%5Csf%28%5Cfrac%7B4x-1%7D%7B5x-2%7D%29%27%3D%5C%5C%5C%5C%5Cfrac%7B%284x-1%29%27%285x-2%29%20-%20%285x-2%29%27%284x-1%29%7D%7B%285x-2%29%5E2%7D%3D%5C%5C%5C%5C%5Cfrac%7B4%285x-2%29%20-%205%284x-1%29%7D%7B%285x-2%29%285x-2%29%7D%3D%5C%5C%5C%5C%5Cfrac%7B20x-8-20x%2B5%7D%7B25x%5E2-2%282%29%285x%29%2B2%5E2%7D%3D%5C%5C%5C%5C%5Cdisplaystyle%20-%5Cfrac%7B3%7D%7B25x%5E2-20x%2B4%7D)
![\sf f'(-1)=-\frac{3}{25(-1)^2-20(-1)+4}\\\\f'(-1)=-\frac{3}{25+20+4}\\\\f'(-1)=-\frac{3}{45+4}\\\\\displaystyle\bf f'(-1)=-\frac{3}{49} \sf f'(-1)=-\frac{3}{25(-1)^2-20(-1)+4}\\\\f'(-1)=-\frac{3}{25+20+4}\\\\f'(-1)=-\frac{3}{45+4}\\\\\displaystyle\bf f'(-1)=-\frac{3}{49}](https://tex.z-dn.net/?f=%5Csf%20f%27%28-1%29%3D-%5Cfrac%7B3%7D%7B25%28-1%29%5E2-20%28-1%29%2B4%7D%5C%5C%5C%5Cf%27%28-1%29%3D-%5Cfrac%7B3%7D%7B25%2B20%2B4%7D%5C%5C%5C%5Cf%27%28-1%29%3D-%5Cfrac%7B3%7D%7B45%2B4%7D%5C%5C%5C%5C%5Cdisplaystyle%5Cbf%20f%27%28-1%29%3D-%5Cfrac%7B3%7D%7B49%7D)
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