C3 Differentiation Urgent Help
Given that y = ln(1+e^x), find that dy/dx and show that (1+e^x)(d^2y/dx^2) = dy/dx.
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
Original post by TheKevinFang
Given that y = ln(1+e^x), find that dy/dx and show that (1+e^x)(d^2y/dx^2) = dy/dx.
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
Multiply the 2nd derivative by , expand the brackets in the numerator and look for cancellation
Original post by GUMI
lnu=1/u
so ln(1+e^x) = 1/(1+e^x) multiplied by the derivative of 1+e^x which is e^x
so (1/(1+e^x))(e^x) = e^x/1+e^x
so ln(1+e^x) = 1/(1+e^x) multiplied by the derivative of 1+e^x which is e^x
so (1/(1+e^x))(e^x) = e^x/1+e^x
?????
Original post by Indeterminate
Multiply the 2nd derivative by , expand the brackets in the numerator and look for cancellation
https://onedrive.live.com/redir?resid=FA1A3849E1FA1C5D!5306&authkey=!AHol3qpCfzmOjZE&v=3&ithint=photo%2cJPG
This is the best I could get - I'm not sure what to do from here, even if it may be painfully obvious...
Original post by TheKevinFang
https://onedrive.live.com/redir?resid=FA1A3849E1FA1C5D!5306&authkey=!AHol3qpCfzmOjZE&v=3&ithint=photo%2cJPG
This is the best I could get - I'm not sure what to do from here, even if it may be painfully obvious...
This is the best I could get - I'm not sure what to do from here, even if it may be painfully obvious...
Noo, don't cancel the brackets containing .
You should expand the numerator and look for two terms that cancel each other out!
Original post by TheKevinFang
Given that y = ln(1+e^x), find that dy/dx and show that (1+e^x)(d^2y/dx^2) = dy/dx.
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
Expand the numerator of your second part and simplify. Then multiply (1+e^x) with the second part, then cancel and you'll get your answer.
(edited 8 years ago)
Original post by TheKevinFang
Given that y = ln(1+e^x), find that dy/dx and show that (1+e^x)(d^2y/dx^2) = dy/dx.
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
dy/dx = e^x/1+e^x
I found that the d^2y/dx^2 = e^x(1+e^x) - e^2x/ (1+e^x)^2.
Can't do the last part though - help please? Will rep
Is this parametric differentiation or am I completely off the hook?
Original post by TeeEm
Am I too late for this thread?
No feel free to go through it as I'm confused as to what the solution is
Original post by RosaA
No feel free to go through it as I'm confused as to what the solution is
I would normally but I am brain dead now.
Original post by TeeEm
I would normally but I am brain dead now.
Don't worry about it ;'D
Original post by Indeterminate
Noo, don't cancel the brackets containing .
You should expand the numerator and look for two terms that cancel each other out!
You should expand the numerator and look for two terms that cancel each other out!
Thanks got it - the e^x's cancel out
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