`(1)/(x)(dy)/(dx)=tan^(-1)x,x!=0`

(dy)/(dx)=1+x tan(y-x)

Solve (1+x^(2))(dy)/(dx)=x+tan^(-1)x

If y=log{((1+x)/(1-x))^(1//4)}-(1)/(2)tan^(-1)x," then "(dy)/(dx)=

(x (dy) / (dx) -y) tan ^ (- 1) ((y) / (x)) = x

y^(2)-(dy)/(dx)=x^(2)(dy)/(dx) A) y^(-1)+tan^(-1)x=c B) x^(-1)+tan^(-1)y=c C) y+tan^(-1)x=c D) x^(-1)+y^(-1)=tan^(-1)x+c

If y=(1)/(a)tan^(-1)((x)/(a))-(1)/(b)tan^(-1)((x)/(b))," then "(dy)/(dx)=

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 .

Find the (dy)/(dx) of y=tan^(-1)((a x-b)/(b x+a))

Find (dy)/(dx) if y=tan^(-1)((sqrt(1+x^(2)-1))/(x)), where x!=0

Find (dy)/(dx) for y=tan^(-1)sqrt((a-x)/(a+x)),-a