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1.Question
Find the value of (f of g)' at the given value of x.
f(u)= (6u)/(u^2+5)
u=g(x)=4x^2+5x+1
x=0
2. The attempt at a solution
f'(u) = (6u) x 1(u^2+5)^(2) x 2u + (u^2+5)^(1) x 6
'= 12u^2 x (u^2+5)^(2) + 6(u^2+5)^(1)
g'(x) = 8x+5
g'(0) = 5
(f of g)'(0) = 12(5)^2 x (5^2 + 5)^(2) + 6(5^2+5)^(1)
= (12x25)/900 + 6/30
= (300/900) + 180/900 = 2/15
Correct answer: 10/3
Thank you ahead of time, I have been working on this simple calculus question for at least 2 hours and just can not get the right answer. I am guessing it is a simple mathematical error in the differentiating somewhere so I have posted it here so hopefully someone could point it out.
Thank you, b0mberman
Find the value of (f of g)' at the given value of x.
f(u)= (6u)/(u^2+5)
u=g(x)=4x^2+5x+1
x=0
2. The attempt at a solution
f'(u) = (6u) x 1(u^2+5)^(2) x 2u + (u^2+5)^(1) x 6
'= 12u^2 x (u^2+5)^(2) + 6(u^2+5)^(1)
g'(x) = 8x+5
g'(0) = 5
(f of g)'(0) = 12(5)^2 x (5^2 + 5)^(2) + 6(5^2+5)^(1)
= (12x25)/900 + 6/30
= (300/900) + 180/900 = 2/15
Correct answer: 10/3
Thank you ahead of time, I have been working on this simple calculus question for at least 2 hours and just can not get the right answer. I am guessing it is a simple mathematical error in the differentiating somewhere so I have posted it here so hopefully someone could point it out.
Thank you, b0mberman
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