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Differention (could you check my solutions please)

  • Thread starter enosthapa
  • Start date
  • #1
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Homework Statement



Differentiate y=e-xsin(3x)

2.The attempt at a solution

With Product rule
y'=-e-xSin(3x)+3e-xCos(3x)

And Logarithm way
Taking log both sides

lny= lne-x+ln(Sin3x)

lny= 1/x+ln(Sin3x)

1/y*dy/dx=-x-2+3(Cos3x/Sin3x)

y'=-(e-xSin3x)/x2+3e-xCos3x
 

Answers and Replies

  • #2
2,544
2
your product rule one looks good , but I don't think log one is .
why do you go from ln(e^-x) to 1/x
dervative of ln(e^(-x)) is -1
 
  • #3
9
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your product rule one looks good , but I don't think log one is .
why do you go from ln(e^-x) to 1/x
dervative of ln(e^(-x)) is -1
I would make sense but this is what i did

ln(e^-x) = 1/(lne^x)
=1/(x.lne)
=1/x
 
  • #4
2,544
2
ok but you see the difference ln(e^-x) = ln(1/(e^x))
 
  • #5
9
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Oh yes thankx..... but can I do
ln(e^-x) = -x lne =-x
 
  • #6
SammyS
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Oh yes thankx..... but can I do
ln(e^-x) = -x lne =-x
Of course!

ln(t) is the inverse function of e(t), so ln(et ) = t .
 

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