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What is the derivative of #y= x/pi#?

Answer 1

Cameron Alexander

For any constant #c# if #y = cx#

then #(dy)/(dx) = c#

Given

#y=x/pi= (1/pi)x#

and while #1/pi# might look like a weird constant, that's all it really is; so

#(dy)/(dx) = 1/pi#

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Answer 2

Aurora Alvarado

It is #1/pi#

Don't let #pi# confuse you. (It's sneaky that way.)

#pi# is just a number. It's a little bigger than 3.

Speaking of which, what is the derivative of #y=x/3#? Well, since #x/3=1/3x# it's the same as the derivative of any other number times #x#. It's just the number. The derivative of #x/3# is #1/3#

Back to the question at hand:

#y=x/pi# is the same as #y=1/pix#.

So the derivative is #y'=1/pi#

Note

It is possible to use the quotient rule for this kind of thing, but it's more involved and more tedious. (And also likely to result in error.)

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Answer 3

Luke Alvarez

The derivative of y = x/π is 1/π.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.