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Can we find the derivative of all functions? [Solved!]

My question

I have a silly question: Is there any function that we can't find the derivative of it ???

Relevant page

Table of Derivatives

What I've done so far

Gone through all the derivatives examples on IntMath. They are very useful!

X

I have a silly question: Is there any function that we can't find the derivative of it ???
Relevant page

<a href="/differentiation-transcendental/table-derivatives.php">Table of Derivatives</a>

What I've done so far

Gone through all the derivatives examples on IntMath. They are very useful!

Re: Can we find the derivative of all functions?

Hi Garrett

It's not a silly question - it's a good one!

In theory, you can differentiate any continuous function using 3. The Derivative from First Principles. The important words there are "continuous" and "function". You can't differentiate in places where there are gaps or jumps and it must be a function (just one y-value for each x-value.)

So you can differentiate `y = 1/x` everywhere except at `x = 0`. (because everywhere else it is a well-behaved function).

You can't do normal differentiation on x^2 + y^2 = 1, which is a circle, since it is not a function. (But we can differentiate it using 8. Differentiation of Implicit Functions).

Hope that helps.

X

Hi Garrett

It's not a silly question - it's a good one!

In theory, you can differentiate any continuous function using <a href="/differentiation/3-derivative-first-principles.php">3. The Derivative from First Principles</a>. The important words there are "continuous" and "function". You can't differentiate in places where there are gaps or jumps and it must be a function (just one y-value for each x-value.)

So you can differentiate `y = 1/x` everywhere except at `x = 0`. (because everywhere else it is a well-behaved function).

You can't do normal differentiation on x^2 + y^2 = 1, which is a circle, since it is not a function. (But we can differentiate it using <a href="/differentiation/8-derivative-implicit-function.php">8. Differentiation of Implicit Functions</a>).

Hope that helps.

Re: Can we find the derivative of all functions?

Thanks - it does

X

Thanks - it does

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