Can dx/dy always be used for integration and derivation on a circle?

[SHOORY]

Homework Statement

is dx/dy= x/y
if yes can i use it always

Homework Equations

for example in a circle
dA/dtheta=A/360

The Attempt at a Solution

if its right sometimes what are the conditions of using it

 

[mjc123]

Generally, no it is not. (You can integrate the expression to find the conditions under which it is true.)

 

[Orodruin]

Generally, no it is not.

And it is quite easy to find counter-examples. For example, let $y = x^2$. Then $dy/dx = 2x \neq y/x = x$.

 

[SHOORY]

And it is quite easy to find counter-examples. For example, let $y = x^2$. Then $dy/dx = 2x \neq y/x = x$.

ok thank you

 

[mjc123]

See the graph below for an illustration. The secant is the line through the origin that cuts the curve at (x,y); its slope is y/x. The tangent is the line that touches the curve at (x,y); its slope is dy/dx, the instantaneous slope of the curve at (x,y), or the rate of change of y with x at that point.