What is the derivative of # pi*r^2#?

1 Answer
Oct 18, 2017

The derivative of #pi * r^2# (assuming that this is with respect to #r#) is
#color(white)("XXX")(d pir^2)/(dr)=color(red)(2pir)#

Explanation:

In general the power rule for differentiating a function of the general form #f(x)=c * x^a# where #c# is a constant
is #(d f(x))/(dx)=a * c *x^(a-1)#

In this case
#color(white)("XXX")#the constant (#c#) is #pi#
#color(white)("XXX")#the exponent (#a#) is #2#
#color(white)("XXX")#and we are using #r# as our variable, instead of #x#

So
#color(white)("XXX")(d (pir^2))/(dr)= 2 * pi * r^(2-1)#

#color(white)("XXXXXXX")=2pir#