Finn F'(x) når:
F(x)=x2^X ?
F(x)= x^2*2^-x
Takk for hjelpen
Derivasjon
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Den deriverte av [tex]a^x[/tex] er [tex](a^x)^\prime = a^x \cdot \ln a[/tex]
ellers er det bare å bruke produktregelen
[tex](x\cdot 2^x)^\prime = 1\cdot 2^x + x \cdot 2^x\cdot \ln 2 = 2^x(x\cdot \ln 2 + 1)[/tex]
[tex](x^2\cdot 2^{-x})^\prime = (\frac{x^2}{2^x})^\prime =\frac{2x\cdot 2^x - x^2\cdot 2^x\cdot \ln 2}{(2^x)^2}=\frac{2^x(2x-x^2\cdot \ln 2)}{(2^x)^2}=\frac{2x-x^2\cdot \ln2}{2^x}[/tex]
ellers er det bare å bruke produktregelen
[tex](x\cdot 2^x)^\prime = 1\cdot 2^x + x \cdot 2^x\cdot \ln 2 = 2^x(x\cdot \ln 2 + 1)[/tex]
[tex](x^2\cdot 2^{-x})^\prime = (\frac{x^2}{2^x})^\prime =\frac{2x\cdot 2^x - x^2\cdot 2^x\cdot \ln 2}{(2^x)^2}=\frac{2^x(2x-x^2\cdot \ln 2)}{(2^x)^2}=\frac{2x-x^2\cdot \ln2}{2^x}[/tex]
Last edited by Olorin on 26/08-2007 20:55, edited 1 time in total.
The square root of Chuck Norris is pain. Do not try to square Chuck Norris, the result is death.
http://www.youtube.com/watch?v=GzVSXEu0bqI - Tom Lehrer
http://www.youtube.com/watch?v=GzVSXEu0bqI - Tom Lehrer