SOLUTION: How I can solve this equation If g(x).f(x)= 4 ; at x=4 , g(4)=2 , g'(4) = 1/4 ; calculate f'(4) ???

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Question 1082385: How I can solve this equation
If g(x).f(x)= 4 ; at x=4 , g(4)=2 , g'(4) = 1/4 ; calculate f'(4) ???
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
At x=4,
g%284%29f%284%29=4
2%2Af%284%29=4
f%284%29=2
and
gf=4
Differentiating implicitly,
g%2A%28df%2Fdx%29%2Bf%2A%28dg%2Fdx%29=0
So at x=4,
2%2A%28df%2Fdx%29%2B2%2A%281%2F4%29=0
2%2A%28df%2Fdx%29=-1%2F2
df%2Fdx=-1%2F4