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

Answer 1

#pi#

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#

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Answer 2

Cameron Alexander

#pi' (x) #

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

and, well, ...

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

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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.