# Integration and derivation

## 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

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mjc123
Homework Helper
Generally, no it is not. (You can integrate the expression to find the conditions under which it is true.)

• Delta2 and SHOORY
Orodruin
Staff Emeritus
Homework Helper
Gold Member
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
Homework Helper
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. #### Attachments

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• SHOORY, Orodruin and Delta2