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Find dx/dy for the following function: y=sinx+5e^.4x dx/dy =

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is it dx/dy?
what does dx/dy equals
I just want to make sure the question, because dx/ dy !=dy/dx

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Other answers:

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

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