Question

This is probably something dumb, But
What is wrong here?
x=0,
Differenciating w.r.t. x,
=> 1 = 0

Answer 1

u differentiate a function, not an equation.

Answer 2

f(x)=x
f'(x)=1
f()=0
f'()=0

Answer 3

x=0 is the y axis.
It's basically a straight line.

Answer 4

or in other words..
d/dx(x) = d/dx (0)
dx/dx=0
dx=0

Answer 5

right, when u differentiate at a point, u find slope of that line.

Answer 6

precisely.
Show should I be getting infinity?

Answer 7

*So shouldn't

Answer 8

u cannot write vertical line as f(x)=.....

Answer 9

I see.
That kinda makes sense.
Thankyou :)

Answer 10

really! ? but u got me thinking.....

Answer 11

Yeah.
I think I get it.
Because you used the word function.
x=0 is not a function of x at all.
Therefore it cant be differenciated w.r.t. x.
Reason being for the same value of x (=0), you have multiple values of y.
Therefore not a function => Limit of the differential doesnt exist (Using calculus definition)
Also, to support this,
We can say that x=0 is a function of y.
As for one value of y you get one x. Therefore differential w.r.t y should exist.
And note here,
dx/dy = 0which is what should have been.

Answer 12

@hartnn Does that convince you?

Answer 13

oh! yesss.....that 'x=0 is not a function' part! why didn't it click me?? i knew that....

Answer 14

thanks @siddhantsharan :D