Before we differentiate, we must know whether a variable in that expression represents a constant or variable, correct?(adsbygoogle = window.adsbygoogle || []).push({});

For example, if we have the function,

[tex]f(x) = r^3 x^2[/tex]

[tex]f'(x) = \frac{d}{{dx}}\left[ {r^3 x^2 } \right][/tex]

(1) Now if [tex]r[/tex] represents avariablethen,

[tex]f'(x) = r^3 \cdot \frac{d}{{dx}}\left[ {x^2 } \right] + \frac{d}{{dx}}\left[ {r^3 } \right] \cdot x^2

[/tex]

[tex]f'(x) = 2r^3 x + 3r^2 x^2[/tex]

But if we know [tex]r[/tex] to be a constant then,

[tex]f'(x) = 2r^3 x[/tex]

So it seems like it is very important to know exactly what the variable represents in a function. Am I correct? In my current calculus textbook, I don't think this topic was covered thoroughly enough.

EDIT: On line labeled (1) the word "constant" was replaced by the intented word, "variable". My mistake...

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# Differentiating Constants

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