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If $s(x)$ and $c(x)$ are differentiable, why does,

$(s + c)' = ss' + cc' $

And not just $s' + c'$

Or am I wrong?

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  • $\begingroup$ Are talking of chain rule? if then google it simply. $\endgroup$ – mnulb Mar 2 '17 at 17:51
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    $\begingroup$ Of course $(s+c)'=s'+c'$. Are you sure it's not $\frac12 (s^2+c^2)'$? $\endgroup$ – Hans Lundmark Mar 2 '17 at 17:55
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You are wrong, Derivative is a linear operator. It follows the following identities

$$ \begin{matrix} (s u)' \equiv s\, u' \\ (u+v)' \equiv u' + v' \end{matrix} $$

where $s$ is a scalar constant, and $u$ and $v$ are functions

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