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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

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

\[Find \frac{ dx }{ dy } for the following function. Y = sinx + 5e ^{0.4x}\]

ok

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

ok

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

http://math.stackexchange.com/questions/292590/is-dx-dy-1-dy-dx-in-calculus

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?

implicitly*

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

\[\large y=\sin x+5e^{0.4x}\]
\[\large 1=(\cos x +2e^{0.4x})\frac{dx}{dy}\]

because calculus is about functions and expansions

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

works*

not just that i will change my proof for Kepler's laws of motion ...