Need calc help 1 last time.

  • #1
hi there i am having trouble on the following question.

1. ln(x+y) = e^3x
(1/x+y)(1+(dy/dx)) = (e^3x)(3)
what can u substititue for y???
 
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Answers and Replies

  • #2
lurflurf
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punjabi_monster said:
hi there i am having trouble on 2 quesitons.

1. ln(x+y) = e^3x
(1/x+y)(1+(dy/dx)) = (e^3x)(3)
what can u substititue for y???
I take it you are finding dy/dx by implict differentiation?
[tex]\log(x+y)=e^{3x}[/tex]
differentiation yeilds
[tex]\frac{1+\frac{dy}{dx}}{x+y}=3e^{3x}[/tex]
solving for dy/dx
[tex]\frac{dy}{dx}=3(x+y)e^{3x}-1[/tex]
observe x+y=exp(exp(3x))
[tex]\frac{dy}{dx}=3e^{e^{3x}}e^{3x}-1[/tex]
simplify
[tex]\frac{dy}{dx}=3e^{3x+e^{3x}}-1[/tex]
observe that one could solve the original equation for y and obtain a more straitforward solution.
[tex]\log(x+y)=e^{3x}[/tex]
solve for y
[tex]y=e^{e^{3x}}-x[/tex]
differentiate
[tex]\frac{dy}{dx}=3e^{e^{3x}}e^{3x}-1[/tex]
 
  • #3
551
1
You're not meant to do people's work for them :/.
 
  • #5
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By solving the natural log.
 
  • #7
HallsofIvy
Science Advisor
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In general, however, when doing an implicit differentiation, it is not necessary nor desirable to solve for y and then substitute that for y in the expression for the derivative. It is better to leave it in terms of both x and y.
 

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