Integration and derivation

  • Thread starter SHOORY
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  • #1
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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
 

Answers and Replies

  • #2
mjc123
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Generally, no it is not. (You can integrate the expression to find the conditions under which it is true.)
 
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  • #3
Orodruin
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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##.
 
  • #4
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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
 
  • #5
mjc123
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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.

tangent & secant.png
 

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