If `y=e^x then dy/dx =`
a) x
b) 0
c) y
d) `1/y`

If e^(-y)*y=x, then (dy)/(dx) is

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

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 (x)/(x-y)=log((a)/(x-y)) then (dy)/(dx) is (a) (x)/(y), (b) 2-(x)/(y), (c) 2, (d) (x-y)/(x)

If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+... , then (dy)/(dx)= a. y+1 b. y-1 c. y d. y^2

If x=logp and y=1/p ,then (a) (d^2y)/(dx^2)-2p=0 (b) (d^2y)/(dx^2)+y=0 (c) (d^2y)/(dx^2)+(dy)/(dx)=0 (d) (d^2y)/(dx^2)-(dy)/(dx)=0

If y=cos^(-1)(cosx),t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2-y^2)/(x^2+y^2) (d) y/x

If y = e^(x) (sin x + cos x ) , prove that (d^(2) y)/( dx^(2)) - 2 (dy)/( dx) + 2 y = 0

If y=x^x prove that (d^2y)/(dx^2)-1/(y)(dy/dx)^2-y/x=0

If y=x^(x) , prove that: (d^(2)y)/(dx^(2))-1/y((dy)/(dx))^(2) - y/x=0