If `x e^(x y)-y=sin^2x` then `(dy)/(dx)a tx=0` is a. 0 b. 1 c. -1 d. none of these

If y=(1+x)^y+sin^-1(sin^2x) , then (dy)/(dx) at x = 0 is

If y=tan^(-1)((sin x+cos x)/(cos x-sin x)), then (dy)/(dx) is equal to (1)/(2)(b)0(c)1(d) none of these

If 8f(x)+6f((1)/(x))=x+5 and y=x^(2)(f(x), then (dy)/(dx) at x=-1 is equal to 0( b) (1)/(14)(c)-(1)/(4)(d) None of these

y=cos^(-1)((5cos x-12sin x)/(13)),wherexin(0,(pi)/(2)) then (dy)/(dx) is.(a)1(b) -1( c) 0 (d) none of these

If y=1/(1+x^(a-b)+x^(c-b))+1/(1+x^(b-c)+x^(a-c))+1/(1+x^(b-a)+x^(c-a)), then (dy)/(dx) is equal to (a)1 (b) (a+b+c)^(x+b+c-1) 0 (d) none of these

int_0^oo (xlogx)/(1+x^2)^2dx= (A) e (B) 1 (C) 0 (D) none of these

If x^(y)=e^(x-y) then (a) (dy)/(dx) doesn't exist at x=1 (b) (dy)/(dx)=0 when x=1 (c) (dy)/(dx)=(1)/(2) when x=e (d) none of these

If ax^(2)+2hxy+by^(2)=0, then (dy)/(dx) is equal to (y)/(x)( b) (x)/(y)(c) ,None of these

If y=e^( sinx ) the value of (dy)/(dx) at x=(pi)/(2) is , (a) 1 , (b) e , (c) 0 ,(d) not defined .

If sin(x+y)=log(x+y), then (dy)/(dx)=(a)2 (b) -2(c)1(d)-1]