anonymous
  • anonymous
how do u find the equation of the tangent line to the curve at the given point: y=e^x/x, (1,e)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1. Take its derivative: \[dy/dx = -e ^{x}/x ^{2} + e ^{x}/x\]
anonymous
  • anonymous
Substitute x = 1
anonymous
  • anonymous
Whatever value you obtain for dy/dx after the substitution, let that represent your m value for the equation y = mx+c

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anonymous
  • anonymous
i got 0 as the slope but then when i plug it in i still get the wrong answer
anonymous
  • anonymous
To solve for the constant 'c', just substitute: x = 1 y = e m =dy/dx (Its numerical value that you obtained) Then, for your final sub in the c and m values
anonymous
  • anonymous
Double check to make sure my derivative is correct
anonymous
  • anonymous
But i'm quite sure the steps are correct though.
anonymous
  • anonymous
ok i got it thanks
anonymous
  • anonymous
Using the derivative presented above, I also get 0 as it's derivative at x=1. If this is the case then the equation of the tangent line at the point (1,e) on the original curve should be y=e.

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