anonymous
  • anonymous
Find dx/dy for the following function: y=sinx+5e^.4x dx/dy =
Calculus1
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
is it dx/dy?
anonymous
  • anonymous
what does dx/dy equals
anonymous
  • anonymous
I just want to make sure the question, because dx/ dy !=dy/dx

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anonymous
  • anonymous
if it is dx/ dy. it's not easy to solve. you must solve for x first , then take derivative respect to y.
anonymous
  • anonymous
it will behave implicitly
anonymous
  • anonymous
i think she means dy/dx
anonymous
  • anonymous
i thought i had to find the derivative and then solve for y
anonymous
  • anonymous
@mathsmind you help her, ok?
anonymous
  • anonymous
no u help her
anonymous
  • anonymous
can u double check the question plz
anonymous
  • anonymous
it must be dy/dx at ur level
anonymous
  • anonymous
\[Find \frac{ dx }{ dy } for the following function. Y = sinx + 5e ^{0.4x}\]
anonymous
  • anonymous
ok
anonymous
  • anonymous
u allowed everyone to escape from this question hehehehe
anonymous
  • anonymous
lol i know, i wish i could escape it too
anonymous
  • anonymous
dx/dy = 1/(dy/dx)
anonymous
  • anonymous
@jim_thompson5910 rescue me please
anonymous
  • anonymous
ok i will solve it all it is implicit differentiation but in terms of x
anonymous
  • anonymous
so when u diff sin(x) it will be cos(x)dx/dy
anonymous
  • anonymous
and y will become 1 when u differentiate it
anonymous
  • anonymous
ok
anonymous
  • anonymous
Just find dy/dx and take the reciprocal.
anonymous
  • anonymous
nope don't do that
anonymous
  • anonymous
they are not the same
anonymous
  • anonymous
Look, dx/dy = 1/(dy/dx)
anonymous
  • anonymous
no it does not work like that
anonymous
  • anonymous
I hope you're kidding. I'm not manipulating fractions
anonymous
  • anonymous
look multiply both sides
anonymous
  • anonymous
u r missing the chain rule this is calculus not algebra
anonymous
  • anonymous
http://math.stackexchange.com/questions/292590/is-dx-dy-1-dy-dx-in-calculus
anonymous
  • anonymous
the case where u use a reciprocal is by using the chain rule and cancelling each term out
anonymous
  • anonymous
Can't you implicit differentiate in this situation?
anonymous
  • anonymous
implicitly*
anonymous
  • anonymous
yes that is different from ur fomula
anonymous
  • anonymous
im even more confused...
anonymous
  • anonymous
he wants u to use L rule
anonymous
  • anonymous
which is similar to what i said about the chain rule
anonymous
  • anonymous
Lebenz derived a formula from the chain rule
anonymous
  • anonymous
\[\large y=\sin x+5e^{0.4x}\] \[\large 1=(\cos x +2e^{0.4x})\frac{dx}{dy}\]
anonymous
  • anonymous
nope i told u don't do that, unless if u want to apply Lebenz rule u need to take the inverse of the function then take the reciprocal ...
anonymous
  • anonymous
because calculus is about functions and expansions
anonymous
  • anonymous
read that carefully If the derivative of y = f(x) is dy/dx, then the derivative of the inverse function which expresses x in terms of y is given by the formula
anonymous
  • anonymous
in other words ur Lebenz works if x= sin(y)+5e^y
anonymous
  • anonymous
so u can take the inverse of the function then apply the rule ok
anonymous
  • anonymous
i told u they are not the same but thanks anyway for bribing the topic up
anonymous
  • anonymous
so take the inverse of the function then use the rule
anonymous
  • anonymous
or solve it implicitly as i started
anonymous
  • anonymous
if the case was simple like this then implicit differentiation would have never exist
anonymous
  • anonymous
\[y = \sin(x) + e^{0.4x} \longrightarrow 1=\frac{dx}{dy}\cos(x)+2\frac{dx}{dy}e^{0.4x}\]
anonymous
  • anonymous
the method u use is solving this in an implicit way
anonymous
  • anonymous
take dx/dy as a common factor
anonymous
  • anonymous
well @Xavier ur method also works congratulation!
anonymous
  • anonymous
so both methods work fine, actually u made me come with a new theory in math, or a different proof for Leben'z formula. although maths is not my major, but i will write a new paper on this and publish it
anonymous
  • anonymous
works*
anonymous
  • anonymous
not just that i will change my proof for Kepler's laws of motion ...

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