lovesit2x
Find dx/dy for the following function:
y=sinx+5e^.4x
dx/dy =
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Hoa
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is it dx/dy?
lovesit2x
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what does dx/dy equals
Hoa
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I just want to make sure the question, because dx/ dy !=dy/dx
Hoa
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if it is dx/ dy. it's not easy to solve. you must solve for x first , then take derivative respect to y.
mathsmind
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it will behave implicitly
mathsmind
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i think she means dy/dx
lovesit2x
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i thought i had to find the derivative and then solve for y
Hoa
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@mathsmind you help her, ok?
mathsmind
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no u help her
mathsmind
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can u double check the question plz
mathsmind
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it must be dy/dx at ur level
lovesit2x
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\[Find \frac{ dx }{ dy } for the following function. Y = sinx + 5e ^{0.4x}\]
mathsmind
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ok
mathsmind
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u allowed everyone to escape from this question hehehehe
lovesit2x
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lol i know, i wish i could escape it too
Xavier
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dx/dy = 1/(dy/dx)
lovesit2x
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@jim_thompson5910 rescue me please
mathsmind
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ok i will solve it all it is implicit differentiation but in terms of x
mathsmind
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so when u diff sin(x) it will be cos(x)dx/dy
mathsmind
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and y will become 1 when u differentiate it
lovesit2x
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ok
Xavier
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Just find dy/dx and take the reciprocal.
mathsmind
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nope don't do that
mathsmind
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they are not the same
Xavier
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Look, dx/dy = 1/(dy/dx)
mathsmind
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no it does not work like that
Xavier
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I hope you're kidding. I'm not manipulating fractions
mathsmind
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look multiply both sides
mathsmind
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u r missing the chain rule this is calculus not algebra
mathsmind
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the case where u use a reciprocal is by using the chain rule and cancelling each term out
Azteck
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Can't you implicit differentiate in this situation?
Azteck
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implicitly*
mathsmind
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yes that is different from ur fomula
lovesit2x
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im even more confused...
mathsmind
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he wants u to use L rule
mathsmind
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which is similar to what i said about the chain rule
mathsmind
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Lebenz derived a formula from the chain rule
Azteck
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\[\large y=\sin x+5e^{0.4x}\]
\[\large 1=(\cos x +2e^{0.4x})\frac{dx}{dy}\]
mathsmind
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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 ...
mathsmind
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because calculus is about functions and expansions
mathsmind
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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
mathsmind
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in other words ur Lebenz works if x= sin(y)+5e^y
mathsmind
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so u can take the inverse of the function then apply the rule ok
mathsmind
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i told u they are not the same but thanks anyway for bribing the topic up
mathsmind
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so take the inverse of the function then use the rule
mathsmind
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or solve it implicitly as i started
mathsmind
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if the case was simple like this then implicit differentiation would have never exist
mathsmind
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\[y = \sin(x) + e^{0.4x} \longrightarrow 1=\frac{dx}{dy}\cos(x)+2\frac{dx}{dy}e^{0.4x}\]
mathsmind
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the method u use is solving this in an implicit way
mathsmind
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take dx/dy as a common factor
mathsmind
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well @Xavier ur method also works congratulation!
mathsmind
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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
mathsmind
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works*
mathsmind
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not just that i will change my proof for Kepler's laws of motion ...