What is the derivative of pi*r^2πr2?

1 Answer
Oct 18, 2017

The derivative of pi * r^2πr2 (assuming that this is with respect to rr) is
color(white)("XXX")(d pir^2)/(dr)=color(red)(2pir)XXXdπr2dr=2πr

Explanation:

In general the power rule for differentiating a function of the general form f(x)=c * x^af(x)=cxa where cc is a constant
is (d f(x))/(dx)=a * c *x^(a-1)df(x)dx=acxa1

In this case
color(white)("XXX")XXXthe constant (cc) is piπ
color(white)("XXX")XXXthe exponent (aa) is 22
color(white)("XXX")XXXand we are using rr as our variable, instead of xx

So
color(white)("XXX")(d (pir^2))/(dr)= 2 * pi * r^(2-1)XXXd(πr2)dr=2πr21

color(white)("XXXXXXX")=2pirXXXXXXX=2πr