If `sqrt(x)` +`sqrt(y)=4,t h e nfin d(dx)/(dy)a ty=1.`

Solve the following differential equation: [(e^(-2)sqrt(x))/(sqrt(x))-(y)/(sqrt(x))](dx)/(dy)=1,x!=0

Statement 1: If e^(xy)+ln(xy)+cos(xy)+5=0, then (dy)/(dx)=-y/x . Statement 2: d/(dx)(xy)=0,y is a function of x implies(dy)/(dx)=-y/x .

Solve the differential equation [(e^(-2sqrt(x)))/(sqrt(x))-(y)/(sqrt(x))](dx)/(dy)=1(x!=0)

The solution of differential equation [ e^(-2sqrt(x))/(sqrt(x))-y/(sqrt(x))](dx)/(dy)=1, (x!=0) is

The solution of the differential equation (e^(-2 sqrt(x))-(y)/(sqrt(x)))(dx)/(dy)=1 is given by

Solve the following differential equation: y sqrt(1+x^(2))+x sqrt(1+y^(2))(dy)/(dx)=0

If y = f(x) and x = g(y), where g is the inverse of f, i.e., g = f^(-1) and if (dy)/(dx) and (dx)/(dy) both exist and (dx)/(dy) ne 0 , show that (dy)/(dx) = (1)/((dx//dy)) . Hence, (1) find (d)/(dx) (tan^(-1)x) (2) If y=sin^(-1)x, -1lexle1, -(pi)/(2)leyle(pi)/(2) , then show that (dy)/(dx)=(1)/(sqrt(1-x^(2))) where |x| lt 1 .

If y=f(x) is a differentiable function x such that invrse function x=f^(-1) y exists, then prove that x is a differentiable function of y and (dx)/(dy)=(1)/((dy)/(dx)) where (dy)/(dx) ne0 Hence, find (d)/(dx)(tan^(-1)x) .