Question

Is there a method for finding the derivative of y=x^2 without using calculus OR LIMITS?

I think I have found a way, but would first like to hear if you have heard of any.

Answer 1

did you take two half derivatives?

Answer 2

I think not (don't know what it is)

Answer 3

If you found another way, you probably did calculus without realizing it..

Answer 4

No, definitely not

Answer 5

Power Rule? Well, that is Calculus too.

Answer 6

No differentiation rules at all

Answer 7

The same method can be applied to y=1/x

Answer 8

Ok, well if no-one else has anything to say, I'll proceed

Answer 9

you have an audience now. may we see the method?

Answer 10

:(

Answer 11

Let D(0,y1) be a point on the y-axis

We want to find the equation of a line such that it passes through the point D and is a tangent to the parabola y=x^2.

The equation can be written in the form:
y=mx+y1

To find where the line and parabola contact, solve simultaneously.
x^2=mx+y1
x^2-mx-y1=0

x= -b±√∆
------
2a

but since it is a tangent, only one point of contact. So ∆=0

x = m/2
m=2x

Tada

Answer 12

Does your method generalize? (past quadratic)

Answer 13

It might, so far only works for x^2 and 1/x

Answer 14

x^2=mx+y1
x^2-mx-y1=0

Aren't these the same?

Answer 15

yes, just rearranging to show clearly what the a,b,c values are

Answer 16

@estudier Try it for 1/x

Answer 17

I will, just trying to get it first...

Answer 18

This is no calculus, right?