Home
Class 12
MATHS
If x^Y = e^[X - Y], prove that dy/dx= lo...

If `x^Y = e^[X - Y]`, prove that `dy/dx= log x/(1+logx)^2`.

Promotional Banner

Similar Questions

Explore conceptually related problems

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

Differentiate the following w.r.t.x. If y^x = e^(y - x) , prove that (dy)/(dx) = ((1 + log y)^2)/(log y)

"If "x^(y)=e^(x-y)," prove that "(dy)/(dx)=(log x)/((1+log x)^(2)).

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

If y = x^y , prove that (dy)/(dx) = (y^2)/(x(1 - y log x))

If x^x + y^x = 1 , prove that : dy/dx = -[(x^x (1+logx) + y^x.logy)/(x.y^((x-1)))]

Find dy/dx if y=log(logx)

If x^y.y^x = 1 , then prove that : dy/dx = (-y (y+x logx))/(x(y log x + x))