Question

implicit differentiation w/ exponential. I'm stuck. 10x^2e^10y + 6y^3e^5x = 8
(my work in reply)

Answer 1

\[10x^2e^{10y}+6y^3e^{5x}=8\]
Is this what the problem looks like? :D
What part you stuck on bloopitybloopbloopbleepblop? Just the whole thing? :D

Answer 2

I believe you take the derivative of both sides, then solve algebraically for y', so:
\[10x^2e^{10y}+6y^3e^{5x}=8\]
\[\frac{ d }{ dx }(10x^2e^{10y}+6y^3e^{5x})=\frac{ d }{ dx }(8)\]
\[\frac{ d }{ dx }(10x^2e^{10y})+\frac{ d }{ dx }(6y^3e^{5x})=0\]
\[20xe^{10y}+10x^210e^{10yy'}+18y^2y'e^{5x}+6y^35e^{5x}=0\]
\[10x^210e^{10yy'}+18y^2y'e^{5x}=-20xe^{10y}-6y^35e^{5x}\]
This is where I'm stuck. If I'm on the right path so far, next I need to factor out y', then divide, so I end up with y' equals something. But here I don't know how to factor out a y' when it is part of an exponent like \[10x^210e^{10yy'}\]

Answer 3

Hmm so the y' shouldn't have gotten stuck in your exponent, I'm not sure how that happened! :) heh

Answer 4

\[(e^{10y})'=e^{10y}(10y)'=e^{10y}(10)y'\]

Answer 5

Understand? <:o

Answer 6

ah, I messed up deriving e again. Guess I see something I need to practice. That was it! Thanks!
\[y' = -\frac{ 20xe^{10y}-6y^35e^{5x} }{ 10x^210e^{10y}+18y^2e^{5x} }\]

Answer 7

yay bloop \c:/