SOLUTION: Given functions f and g satisfying f(3) = 3, g(3) = 2, f ′(3) = 4 and g ′(3) = 2 find the values of the following derivatives. (f . g)′(3) = (f

Algebra ->  Exponents -> SOLUTION: Given functions f and g satisfying f(3) = 3, g(3) = 2, f ′(3) = 4 and g ′(3) = 2 find the values of the following derivatives. (f . g)′(3) = (f      Log On


   

Question 987646: Given functions f and g satisfying
f(3) = 3, g(3) = 2, f ′(3) = 4 and g ′(3) = 2
find the values of the following derivatives.
(f . g)′(3) =
(f / g)′(3) =
THANK YOU :-)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
(f * g)(x) = f(x)*g(x)


(f * g)'(x) = [f(x)*g(x)]' ... apply the derivative


(f * g)'(x) = f ' (x)*g(x) + f(x)*g ' (x) ... use the product rule


(f * g)'(3) = f ' (3)*g(3) + f(3)*g ' (3) ... plug in x = 3


(f * g)'(3) = 4*2 + 3*2 ... make the proper substitutions (based on the values given)


(f * g)'(3) = 8+6


(f * g)'(3) = 14


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(f/g)(x) = f(x)/g(x)


(f/g)'(x) = [f(x)/g(x)]' ... apply the derivative


(f/g)'(x) = [f ' (x)*g(x) - f(x)*g ' (x)]/[g(x)]^2 ... use the quotient rule


(f/g)'(3) = [f ' (3)*g(3) - f(3)*g ' (3)]/[g(3)] ... plug in x = 3


(f/g)'(3) = [4*2 - 3*2]/[2^2] ... make the proper substitutions (based on the values given)


(f/g)'(3) = (8-6)/4


(f/g)'(3) = 2/4


(f/g)'(3) = 1/2