Mathematics
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OpenStudy (anonymous):
derivative of
f(x)= 56x/(x^2;4)^2
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OpenStudy (anonymous):
Use the quotient rule.
OpenStudy (anonymous):
\[
\left(\frac{f}{g}\right)' = \frac{f'g-fg'}{g^2}
\]
OpenStudy (anonymous):
yea i did and i keeping getting wrong anser
OpenStudy (anonymous):
answer
OpenStudy (anonymous):
what is \(f\) and \(g\)?
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OpenStudy (anonymous):
56x/(x^2+4)^2
OpenStudy (abb0t):
You could also use product rule if you feel more comfortable using that. Remember: \(\frac{ 1 }{ (a+b)^n } = (a+b)^{-n}\)
OpenStudy (anonymous):
I know, so what is \(f'\) and \(g'\)?
OpenStudy (anonymous):
56 and 2x
OpenStudy (anonymous):
Nope, your \(g'\) is wrong.
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OpenStudy (anonymous):
You either have to expand it, or use the chain rule.
OpenStudy (anonymous):
ohhhhhh
OpenStudy (anonymous):
3x^3+32x
OpenStudy (anonymous):
I need to see your steps
OpenStudy (anonymous):
(x^2+4)^2
(x^2+4)(x^2+4)
x^4+4x^2+4x^2+16
x^4+8x^2+16
3x^2+16x
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OpenStudy (anonymous):
you messed up on \((x^4)'\)
OpenStudy (anonymous):
4x^3
OpenStudy (anonymous):
Alright, now you can use the quotient rule.
OpenStudy (anonymous):
(56)(x^2+4)^2-(56)(4x^3+16)/((x^2+4)^2)^2
OpenStudy (anonymous):
you want 56x on the second term
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OpenStudy (anonymous):
ops
OpenStudy (anonymous):
then simplify a bit and you're done.
OpenStudy (anonymous):
simplyging is the problem !