If `y=a^(x^(y)), then (dy)/(yx)=`

If x^(y) + y^(x) = a^(b) then prove that (dy)/(dx)=-[(yx^(y-1)+y^(x)Logy)/(x^(y)Logx+xy^(x-1))] .

Show that if x^(y)+y^(x)=m^(n) , then : dy/dx=-(y^(x)logy+yx^(y-1))/(x^(y)logx+xy^(x-1)) .

Find the general solutions of the following differential equations. (i) (dy)/(dx) = e^(x+y) (ii) (dy)/(dx) = e^(y-x) (iii) (dy)/(dx) = (xy+y)/(yx+x) (iv) y(1+x)dx+x(1+y)dy = 0

Show that if x^y + y^x = m^n , then: dy/dx = - (y^x logy +yx^(y-1))/(x^y log x + xy^(x-1))

If x^y+y^x= (x+y)^(x+y) , then prove that dy/dx= ((x+y)^(x+y) [1+log(x+y)]-yx^(y-1)-y^xlogy)/(x^ylogx+xy^(x-1) -(x+y)^(x+y) [1+log(x+y)]

Suppose g(x) satisfies g(x)=x+int_(0)^(1)(xy^(2)+yx^(2))g(y)dy , then g(x) is

yx (dy) / (dx) = a (y ^ (2) + (dy) / (dx))

x ^ (2) yx ^ (3) (dy) / (dx) = y ^ (4) cos x