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Need calc help 1 last time.

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???
 
Last edited:

lurflurf

Homework Helper
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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]
 
551
1
You're not meant to do people's work for them :/.
 
how do u get e^e^3x
 
113
1
By solving the natural log.
 
ok thanks guys.
 

HallsofIvy

Science Advisor
Homework Helper
41,712
876
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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