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Given that f(5)=4, f'(5)=5, g(5)=9, g'(5)=8 Calculate (fg)'(5), (f/g)'(5), (g/f)'(5)

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masterpiece56 | Student | Honors

Posted March 7, 2012 at 1:56 AM via web

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Given that f(5)=4, f'(5)=5, g(5)=9, g'(5)=8

Calculate (fg)'(5), (f/g)'(5), (g/f)'(5)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 7, 2012 at 2:06 AM (Answer #1)

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It is given that f(5)=4, f'(5)=5, g(5)=9, g'(5)=8

(fg)'(5) = f'(5)*g(5) + f(5)*g'(5) = 5*9 + 4*8 = 45 + 32 = 77

(f/g)'(5) = (f'(5)*g(5) - f(5)*g'(5))/(g(5))^2 = (5*9 - 4*8)/81 = (45 - 32)/81 = 13/81

(g/f)'(5) = (g'(5)*f(5) - g(5)*f'(5))/(f(5))^2 = (8*4 - 9*5)/(25) = -13/25

The result for (fg)'(5) = 77, (f/g)'(5) = 13/81 and (g/f)'(5) = -13/25

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