Question

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

Answer 1

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`