My calc class is studying basic derivatives, and I'm stuck on a problem.

The problem is f(r) = (4/3) * pi * r^{3}The answer is 4pir^{2}

[tex]\dfrac{d}{dr}\, \left[\dfrac{4\pi r^3}{3}\right][/tex]

. . .[tex]=\, \dfrac{4\pi}{3}\, \cdot\, \dfrac{d}{dr}\left[r^3\right][/tex]

. . .[tex]=\, \dfrac{4\pi\, \cdot\, 3r^2}{3}[/tex]

. . .[tex]=\, 4\pi r^2[/tex]

I understand that the power rule calls for the exponent of 3 to be brought to the front and then the exponent is decreased by one. I also understand that the 3 in the denominator cancels out with the 3 in the numerator.

What I don't understand is why the constant rule (that the derivative of a constant is equal to 0) doesn't apply to the 4 and pi in this case.

Could someone please help explain this? Many thanks.

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