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gx_fx [2016/01/25 13:35] nikolaj |
gx_fx [2016/01/26 15:13] nikolaj |
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| ==== Function ==== | ==== Function ==== | ||
| | @#55CCEE: context | @#55CCEE: $ f,g : {\mathbb R} \to {\mathbb R} $ | | | @#55CCEE: context | @#55CCEE: $ f,g : {\mathbb R} \to {\mathbb R} $ | | ||
| - | | @#FF9944: definition | @#FF9944: $ x\mapsto g(x)^{f(x)}$ | | + | | @#FF9944: definition | @#FF9944: $ x\mapsto g(x)^{f(x)}:??$ | |
| ----- | ----- | ||
| === Theorem === | === Theorem === | ||
| - | $\dfrac{{\mathrm d}}{{\mathrm d}x} g(x)^{f(x)} = \left(f(x)\,g'(x) + f'(x)\,g(x)\cdot \log\,g(x)\right)\cdot g(x)^{f(x)-1} $ | + | $\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 == | == Special cases == | ||
| Line 16: | Line 16: | ||
| === Reference === | === Reference === | ||
| ----- | ----- | ||
| - | === Subset of === | + | === Element of === |
| [[Function]] | [[Function]] | ||
