If e^x+e^y=e^(x+y) , prove that (dy)/(dx...

If `e^x+e^y=e^(x+y)` , prove that `(dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1))` or, `(dy)/(dx)+e^(y-x)=0`

Text Solution

AI Generated Solution

Topper's Solved these Questions

DIFFERENTIALS, ERRORS AND APPROXIMATIONS
RD SHARMA ENGLISH|Exercise All Questions|107 Videos
DIRECTION COSINES AND DIRECTION RATIOS
RD SHARMA ENGLISH|Exercise All Questions|90 Videos

Similar Questions

Explore conceptually related problems

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)+e^(y-x)=0

If e^x+e^y=e^(x+y),p rov e t h a t(dy)/(dx)+e^(y-x)=0

If x=e^(x//y) , prove that (dy)/(dx)=(x-y)/(xlogx)

If x=e^(x/y) ,prove that (dy)/(dx)=(x-y)/(xlogx)

If y=e^x+e^(-x) , prove that (dy)/(dx)=sqrt(y^2-4)

If y=e^x+e^-x , prove that (dy)/(dx)=sqrt(y^2-4)

Solve : (dy)/(dx)=e^(x+y)

If x = e^(x//y) , then prove that (dy)/(dx) = (x-y)/(xlogx) .

If x^y=e^(x-y), show that (dy)/(dx)=(logx)/({log(x e)}^2)

RD SHARMA ENGLISH-DIFFERENTIATION-All Questions

Differentiate sin^(-1)sqrt(1-x^2) with respect to cot^(-1)(x/sqrt(1...
Text Solution
|
If ysqrt(x^2+1)=log(sqrt(x^2+)1-x),s howt h a t(x^2+1)(dy)/(dx)+x y+1=...
Text Solution
|
If e^x+e^y=e^(x+y) , prove that (dy)/(dx)=-(e^x(e^y-1))/(e^y(e^x-1)) o...
Text Solution
|
If y=xsin(a+y),p rov et h a t(dy)/(dx)=(sin^2(a+y))/(sin(a+y)-ycos(a+y...
Text Solution
|
If x ylog(x+y)=1,p rov e \ t h a t \ (dy)/(dx)=-(y(x^2y+x+y))/(x(x y^2...
Text Solution
|
If y=(sinx-cosx)^(sinx-cosx) ,pi/4 ltxlt (3pi)/ 4 find dy/dx
Text Solution
|
If y=log((x^2+x+1)/(x^2-x+1))+2/(sqrt(3))t a n^(-1)((sqrt(3)x)/(1-x^2)...
Text Solution
|
If (x-y)e^(x/(x-y))=a , prove that (dy)/(dx)+x=2ydot
Text Solution
|
Differentiate the following functions with respect to x : (e^xlogx)/...
Text Solution
|
Differentiate the following functions with respect to x: log(x+sqrt...
Text Solution
|
Differentiate the following functions with respect to x : tan(e^(s...
Text Solution
|
Differentiate sin^(-1){(2^(x+1). 3^x)/(1+(36)^x)}"w i t hr e s p e...
Text Solution
|
Differentiate the following functions with respect to x: log((sinx)...
Text Solution
|
If y=tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))},"f i n d"(d...
Text Solution
|
Differentiate the following function sqrt((1+sinx)/(1-sinx))
Text Solution
|
If the derivative of tan^(-1)(a+b x) take the value of 1 at x=0,...
Text Solution
|
Differentiate the following functions with respect to x: e^(3x)cos2...
Text Solution
|
If y=sin[2t a n^(-1){sqrt((1-x)/(1+x))}],"f i n d"(dy)/(dx)
Text Solution
|
Differentiate (logx)^x with respect to logxdot
Text Solution
|
Differentiate log(1+x^2) with respect to tan^(-1)xdot
Text Solution
|