What is the derivative of #pi(x)#?

2 Answers
Aug 4, 2016

#pi#

Explanation:

Don't let the symbol #pi# confuse you. Remember that #pi# is just a number, roughly equivalent to #3.14#. If it helps, replace #pi# with #3.14#, to remind you that you're really taking the derivative of #3.14x#.

Recall that the derivative of a constant times #x# is the constant; this is because something like #pix# is a linear equation with constant slope. And since derivative is slope, a linear equation has a constant (i.e. numerical) derivative.

You can also find the result using the power rule:
#d/dxpix^1#
#=1*pix^(1-1)#
#=pix^0#
#=pi-># any number (except 0) to the zero power is #1#

Aug 4, 2016

#pi' (x) #

Explanation:

unless #pi(x)# is a function in which case, hilarious

and, well, ...

#d/dx pi(x) = pi' (x) = d/dx pi(x)#