Question

Need HELP!

Answer 1

if
x ln(y) - y ln(x) = 1 then
prove\[[\frac{ dy }{ dx}]_{x=1} = e( e -1)\]

Answer 2

@phi , @ganeshie8 , @hartnn could u guys lend me a hand

Answer 3

@tukitw

Answer 4

This looks like you should use implicit differentiation

Answer 5

huh.... I study Calculus in my mother language and therefor i don't understan some specific terms in calculus :/ but I can understand the steps... could u pls continue ?

Answer 6

\(\dfrac{d}{dx}\left(x\cdot f(x)\right) = x\left(\dfrac{d}{dx}f(x)\right) + \left(\dfrac{d}{dx}x\right)f(x)\)

By the Product Rule. Let's see what you get.

Answer 7

ok ... i can go as far as here ....

Answer 8

\[\frac{ dy }{ dx } = \frac{ \frac{ y }{ x } - lny }{ \frac{ x }{ y } - \ln x}\]

Answer 9

replace x with 1

Answer 10

how to remove y from this ?

Answer 11

your answer is in terms of y. to get rid of the y
use
x ln(y) - y ln(x) = 1 evaluated at x=1 to solve for y

Answer 12

I think there is something to do with this