Question 987646
(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