My Math Forum chain rule- constant rule

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 July 28th, 2013, 07:32 AM #1 Senior Member   Joined: Oct 2012 Posts: 460 Thanks: 0 chain rule- constant rule Please, How do we get constant rule as a VARIATION OF CHAIN RULE???? Many thanks!!!
 July 30th, 2013, 06:10 PM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: chain rule- constant rule Why should we? The "constant rule" (I assume you mean "the derivative of a constant function is 0 for all x") is much more fundamental than the chain rule. I suppose you could argue that, if f(x)= a for all x, then h(x)= f(g(x))= a for all x and any g. By the chain rule, $\frac{dh}{dx}= \frac{df}{dg}\frac{dg}{dx}$. But clearly, h(x)= f(x) for all x so $\frac{dh}{dx}= \frac{df}{dx}$. That is, we have $\frac{df}{dx}= \frac{df}{dx}\frac{dg}{dx}$ for all g. Since $\frac{dg}{dx}= 1$ for all functions, g, is NOT true, we must have $\frac{df}{dx}= 0$. But that seems like using a sledgehammer to kill a fly.

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