Mathmatical question

[becomingagodo]

Does x^0=1 or x^0=0
I came across a person in a youtube video trying to explain calculus, well tried to explain the idea of why number vanish when taking derivative.

He gave 5^1 as a example, he said the derivative is (1)5^0, which then changes five into zero. Then he gave x as a example and said x^1, then he took the derivative and is was (1)x^0, he then said the derivative equals 1. Anyone?

Seriously confusing, how can x be treated differently to 5 when taking a derivative.

[fls]

Does x^0=1 or x^0=0
I came across a person in a youtube video trying to explain calculus, well tried to explain the idea of why number vanish when taking derivative.

He gave 5^1 as a example, he said the derivative is (1)5^0, which then changes five into zero. Then he gave x as a example and said x^1, then he took the derivative and is was (1)x^0, he then said the derivative equals 1. Anyone?

Seriously confusing, how can x be treated differently to 5 when taking a derivative.

It's not 5^1, but 5(x^0). The derivative then becomes 0*5.

Linda

[Ivor the Engineer]

Further to what Linda said: Derivatives have to be taken with respect to something. E.g.,

f(x) = 5

is actually:

f(x) = 5(x^0)

So the differential of f(x) with respect to x is:

df(x)/dx = 5(0) = 0

[Ziggurat]

Does x^0=1 or x^0=0

x0 = 1.

He gave 5^1 as a example, he said the derivative is (1)5^0, which then changes five into zero.

Derivatives can only be taken with respect to some variable, and which variable you take the derivative with respect to can change what the derivative is. This isn't made explicit in what you write, and possibly not in the presentation you refer to, but it's always true. 51 is not a variable, it's a constant. Because it contains no dependence upon any variable, taking the derivative with respect to any variable will leave you with zero.

Let's say y = x2, and x = z2, so that y = z4. What's the derivative of y? Well, you can't answer that, unless you know which variable to take the derivative with respect to. dy/dx = 2x, but dy/dz = 4z3. So dy/dx does not equal dy/dz.

Now let's go back to 51. Let's take the derivative with respect to x: d(51)/dx = 0 because there's no x dependence there.

Seriously confusing, how can x be treated differently to 5 when taking a derivative.

Because one is a variable, and one isn't. A derivative is a measure of how much a quantity changes when the variable you're taking the derivative with respect to changes. x changes when you change x (not surprising). x2 changes when you change x. But 51 does not change when you change x, so its derivative with respect to x is zero. And since x0 = 1 for all x, x0 doesn't change when you change x either, and its derivative is also zero.

[The Grave]

When you have d(5)/dx, you are asking:"How does y=5 change with respect to the change of x?"

Well, y=5, does not change so d(5)/dx = 0. That is to say no + or - change in the 'y' direction; in other words you have a flat line.

OR: d(5)/dx = 5/ infinity = 0. As dx in the x direction (for the line y=5) is an infinite progression.

It's not what I say; It's the way that I say it!

Griff...

I should really be charging you for this....


10^3 = 1*10*10*10 = 1000
10^2 = 1*10*10..... = 100
10^1 = 1*10.......... = 10
10^0 = 1*(no 10's) = 1

Gcse stuff. Or 'O' level.

[jsfisher]

Be careful, though. 00 isn't so clearly defined.

[The Grave]

In terms of whole powers, 0^n, is zero. Your basically asking; how many zeros do you want me to multiply 'one' by? To get zero.

And 0^(0.5) would be 0.

Simple proofs of a bigger story.

Griff.

[Just thinking]

And just for fun,
0! = 1.

[Paul C. Anagnostopoulos]

The identity for multiplication being 1, don't you know.

~~ Paul

[rwguinn]

When you have d(5)/dx, you are asking:"How does y=5 change with respect to the change of x?"

Well, y=5, does not change so d(5)/dx = 0. That is to say no + or - change in the 'y' direction; in other words you have a flat line.

OR: d(5)/dx = 5/ infinity = 0. As dx in the x direction (for the line y=5) is an infinite progression.

It's not what I say; It's the way that I say it!

Griff...

I should really be charging you for this....


10^3 = 1*10*10*10 = 1000
10^2 = 1*10*10..... = 100
10^1 = 1*10.......... = 10
10^0 = 1*(no 10's) = 1

Gcse stuff. Or 'O' level.
Or for the calculus challanged, but algebraicly semi-literat6e:
The derivative of a function is the instantaneous slope of the curve of that function.
Or another way, the rate of change of that function with repect to the variable..
Which, by definition, must have 2 variables so you can get a slope.