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Advanced Math/implicit differentiation
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Question
find dy/dx.
1) ln y=e^ysinx
2) e^2x=sin(x+3y)
1)
y'/y =( y'sinx + ycosx) e^ysinx
y' = (yy'sinx)(e^ysinx) + (y^2 cosx)(e^ysinx)
y'-(yy'sinx)(e^ysinx)=(y^2 cosx)(e^ysinx)
y'(1-(ysinx)(e^ysinx))=(y^2 cosx)(e^ysinx)
y' = (y^2 cosx)(e^ysinx)/(1-(ysinx)(e^ysinx))
2)
2e^2x = (1+3y')cos(x+3y)
2e^2x - cos(x+3y) = 3y'cos(x+3y)
y' = (2e^2x - cos(x+3y))/3cos(x+3y)
y' = 2e^2x/3cos(x+3y) - 1/3
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Answers by Expert:
Socrates
Expertise
I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.
Experience
Ph.D. in Mathematics and many years teaching undergraduate courses at three state universities.
Education/Credentials
B.S. , M.S. , Ph.D.
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