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What is the derivative of $π \cdot r^{2}$ $pi*r^2$ ?

1 Answer

Oct 18, 2017

The derivative of $π \cdot r^{2}$ $pi * r^2$ (assuming that this is with respect to $r$ $r$ ) is
$XXX \frac{d π r^{2}}{d r} = 2 π r$ $color(white)("XXX")(d pir^2)/(dr)=color(red)(2pir)$

Explanation:

In general the power rule for differentiating a function of the general form $f (x) = c \cdot x^{a}$ $f(x)=c * x^a$ where $c$ $c$ is a constant
is $\frac{d f (x)}{d x} = a \cdot c \cdot x^{a - 1}$ $(d f(x))/(dx)=a * c *x^(a-1)$

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

So
$XXX \frac{d (π r^{2})}{d r} = 2 \cdot π \cdot r^{2 - 1}$ $color(white)("XXX")(d (pir^2))/(dr)= 2 * pi * r^(2-1)$

$XXXXXXX = 2 π r$ $color(white)("XXXXXXX")=2pir$

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