- anonymous

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

- chestercat

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- anonymous

is it dx/dy?

- anonymous

what does dx/dy equals

- anonymous

I just want to make sure the question, because dx/ dy !=dy/dx

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## More answers

- 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

it will behave implicitly

- anonymous

i think she means dy/dx

- anonymous

i thought i had to find the derivative and then solve for y

- anonymous

@mathsmind you help her, ok?

- anonymous

no u help her

- anonymous

can u double check the question plz

- anonymous

it must be dy/dx at ur level

- anonymous

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

- anonymous

ok

- anonymous

u allowed everyone to escape from this question hehehehe

- anonymous

lol i know, i wish i could escape it too

- anonymous

dx/dy = 1/(dy/dx)

- anonymous

@jim_thompson5910 rescue me please

- anonymous

ok i will solve it all it is implicit differentiation but in terms of x

- anonymous

so when u diff sin(x) it will be cos(x)dx/dy

- anonymous

and y will become 1 when u differentiate it

- anonymous

ok

- anonymous

Just find dy/dx and take the reciprocal.

- anonymous

nope don't do that

- anonymous

they are not the same

- anonymous

Look, dx/dy = 1/(dy/dx)

- anonymous

no it does not work like that

- anonymous

I hope you're kidding. I'm not manipulating fractions

- anonymous

look multiply both sides

- anonymous

u r missing the chain rule this is calculus not algebra

- anonymous

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

- anonymous

the case where u use a reciprocal is by using the chain rule and cancelling each term out

- anonymous

Can't you implicit differentiate in this situation?

- anonymous

implicitly*

- anonymous

yes that is different from ur fomula

- anonymous

im even more confused...

- anonymous

he wants u to use L rule

- anonymous

which is similar to what i said about the chain rule

- anonymous

Lebenz derived a formula from the chain rule

- anonymous

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

- 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

because calculus is about functions and expansions

- 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

in other words ur Lebenz works if x= sin(y)+5e^y

- anonymous

so u can take the inverse of the function then apply the rule ok

- anonymous

i told u they are not the same but thanks anyway for bribing the topic up

- anonymous

so take the inverse of the function then use the rule

- anonymous

or solve it implicitly as i started

- anonymous

if the case was simple like this then implicit differentiation would have never exist

- anonymous

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

- anonymous

the method u use is solving this in an implicit way

- anonymous

take dx/dy as a common factor

- anonymous

well @Xavier ur method also works congratulation!

- 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

works*

- anonymous

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

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