- $(c)'=0$, namely the derivative of a constant is 0.
- $(x^n)'=nx^{n-1}$, for any constant $n$ (a.k.a., the power rule).
If $n$ is a non-negative
integer, this makes sense for all values of $x$. If $n$ is a negative
integer, this makes sense for all $x \ne 0$, and if $n$ is a (positive
or negative) fraction, then this makes sense for $x>0$.
-
$(cf(x))'=c\cdot f'(x)$, if $c$ is a constant.
-
$\left(f(x)+g(x)\right)'=f'(x)+g'(x)$
and $\left(f(x)-g(x)\right)'=f'(x)-g'(x)$.
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