Use implicit differentiation to find (dc)/(dv) when v=sqrt(c^2+v^2)

Sanai Ball

Sanai Ball

Answered question

2022-09-27

Use implicit differentiation to find d c d v when v = c 2 + v 2

I know I can solve this using normal implicit methods however I was wondering, why can I not square this so it becomes v 2 = c 2 + v 2 and then simplify so c 2 = 0 c = 0 then the derivative of this is just c = 0, what is flawed?

Answer & Explanation

Leslie Braun

Leslie Braun

Beginner2022-09-28Added 7 answers

There is no flaw in your method. Even if you use implicit differentiation, you will get:
d v = c d c c 2 + v 2 + v d v c 2 + v 2
now use c 2 + v 2 = v to get
d v = c v d c + d v d c = 0
Which is the same as you got squaring both the sides.
Riya Andrews

Riya Andrews

Beginner2022-09-29Added 4 answers

Notice that c ( v ) = 0, because v 2 = c 2 + v 2 directly implies c = 0.
Thus, d c d v = 0 . Your reasoning is fine.

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