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

May 15, 2015

For any constant $c$
if $y = c x$

then $\frac{\mathrm{dy}}{\mathrm{dx}} = c$

Given

$y = \frac{x}{\pi} = \left(\frac{1}{\pi}\right) x$

and while $\frac{1}{\pi}$ might look like a weird constant, that's all it really is;
so

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{\pi}$

May 15, 2015

It is $\frac{1}{\pi}$

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 $y = \frac{x}{3}$? Well, since $\frac{x}{3} = \frac{1}{3} x$ it's the same as the derivative of any other number times $x$. It's just the number.
The derivative of $\frac{x}{3}$ is $\frac{1}{3}$

Back to the question at hand:

$y = \frac{x}{\pi}$ is the same as $y = \frac{1}{\pi} x$.

So the derivative is $y ' = \frac{1}{\pi}$

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.)