Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

If $e^{x+y}=xy,$ what is $\large\frac{dy}{dx}$?

$\begin{array}{1 1}(A)\;\large\frac{y(1-x)}{x(y-1)}\\(B)\;\large\frac{y(1+x)}{x(y-1)}\\(C)\;\large\frac{y(1-x)}{x(1+y)}\\(D)\;\large\frac{y(1+x)}{x(1-y)}\end{array}$

1 Answer

Comment
A)
Given $e^{x+y} = xy$
Taking log on both sides, we get: $ (x+y) \log_e e = \log_e x + \log_e y$
$\Rightarrow x+y = \log_e x + \log_e y$
Differentiating, we get: $dx + dy = \large\frac{1}{x}$$dx + \large\frac{1}{y}$$dy$
Rearranging, we get: $\large\frac{dy}{dx}$$(1 - \large\frac{1}{y}$$) = \large\frac{1}{x}$$-1$
$\Rightarrow \large\frac{dy}{dx} $$ = \large\frac{y(1-x)}{x(y-1)}$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.
...