===== g(x)^f(x) =====
==== Function ====
| @#55CCEE: context     | @#55CCEE: $ f,g : {\mathbb R} \to {\mathbb R} $ |
| @#FF9944: definition  | @#FF9944: $ x\mapsto g(x)^{f(x)}:??$ |

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=== Theorem ===
$\dfrac{{\mathrm d}}{{\mathrm d}x} g(x)^{f(x)} = \left[f(x)\,g'(x) + f'(x)\,g(x)\cdot \log\left(g(x)\right)\right]\cdot g(x)^{f(x)-1} $

== Special cases ==

$\dfrac{{\mathrm d}}{{\mathrm d}x} x^c = c\cdot x^{c-1}$

$\dfrac{{\mathrm d}}{{\mathrm d}x} c^x = \log(c) \cdot c^x$

=== Reference ===
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=== Element of ===
[[Function]]