anonymous
  • anonymous
If \frac(x^2)(64) + \frac (y^2)(25) = 1 and y( 2 ) = 4.84 , find y'( 2 ) by implicit differentiation.
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
Okay, so what do you get when you differentiate the first equation?
anonymous
  • anonymous
2x/64
anonymous
  • anonymous
It should still be an equation.

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anonymous
  • anonymous
2x/64+(2yy')/25
anonymous
  • anonymous
=1
anonymous
  • anonymous
\[\frac d {dx} 1 = 1 \]Oh?
anonymous
  • anonymous
no it wasn't
anonymous
  • anonymous
the problem was changed on me so now its If \frac(x^2)(25) + \frac (y^2)(16) = 1 and y( 1 ) = 3.92 , find y'( 1 ) by implicit differentiation
anonymous
  • anonymous
Okay, so what is your equation after differentiating.
anonymous
  • anonymous
2x/25+2yy'/16=0
anonymous
  • anonymous
now, what is \(x\)?
anonymous
  • anonymous
You need to plug in the values of \(x\) and \(y\)
anonymous
  • anonymous
2/25+2(4.84)y'/16=0
anonymous
  • anonymous
Now solve for \(y'\).
anonymous
  • anonymous
I'm not going to get a medal, am I?
mathstudent55
  • mathstudent55
\( \dfrac{x^2}{25} + \dfrac {y^2}{16} = 1 \) \( \dfrac{2x}{25} + \dfrac{2yy'}{16} = 0 \) \( \dfrac{2(1)}{25} + \dfrac{2(3.92)y'}{16} = 0 \) \( \dfrac{2(3.92)y'}{16} = -\dfrac{2}{25} \) \( y' = -\dfrac{2(16)}{25(2)(3.92) } \) \( y' = -\dfrac{8}{49 } \)

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