Matematik A/Differentialregning: Forskelle mellem versioner
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Regneregler for differentialkvotient |
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== Tre-trins reglen ==
== Regneregler for differentialkvotient ==
Hvis <math>f(x)</math> og <math>g(x)</math> er differentiable funktioner, kan man opstille og vise følgende regler:
<math>(f(x)+g(x))^{\prime}=\frac{d(f(x)+g(x))}{dx}=\frac{d(f(x))}{dx}+\frac{d(g(x))}{dx}=f^{\prime}(x)+g^{\prime}(x)</math>
<math>(f(x)-g(x))^{\prime}=\frac{d(f(x)-g(x))}{dx}=\frac{d(f(x))}{dx}-\frac{d(g(x))}{dx}=f^{\prime}(x)-g^{\prime}(x)</math>
<math>(f(x) \cdot g(x))^{\prime}=\frac{d(f(x) \cdot g(x))}{dx}=f^{\prime}(x) \cdot g(x)+f(x) \cdot g^{\prime}(x)</math>
<math>(\frac{f(x)}{g(x)})^{\prime}=\frac{d(\frac{f(x)}{g(x)})}{dx}=\frac{f^{\prime}(x) \cdot g(x)-f(x) \cdot g^{\prime}(x)}{g(x)^2}</math>
== Den rette linje ==
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