If `xe^(xy)=y+sin^2x` then at `x=0` `(dy)/dx=`

If ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))_(1,0) is equal to

If cos ( xy) = x , show that (dy)/(dx) = -((1+ y sin (xy)))/(x sin xy)

"If "xy+y^(2)=tan x + y," then find "(dy)/(dx).

If y= sin^(-1)x , show that (1-x^(2)) (d^(2)y)/(dx^(2))-x(dy)/(dx)0 .

(i)If y = x^(3) + x^(2) + x +1 then dy/dx at x = 1 is 0 (ii)If y=sin^(-1)((2x)/(1+x^(2))) then dy/dx = tanx (iii) y = x^(x) dy/dx = x^(x)[1+logx] (iv) y = tan^(-1)x, dy/dx = 1/(1 + x^(2) state which pair of the statement given above are true.

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

Consider the equation (x^(3)+y^(3))dx-xy^(2)dy=0 i . Express this equation in the form (dy)/(dx)=(f(x,y))/(g(x,y))

(dy)/(dx) = 3y cot x = sin 2x, y = 2 when x = (pi)/(2)

(x - y)dy - (x + y) dx = 0