Beregn ddx[xx]\displaystyle \frac{d}{dx}[x^x]dxd[xx] ved x=1x = 1x=1.
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f(x)=xxf(x) = x^xf(x)=xx. lnf=xlnx\ln f = x\ln xlnf=xlnx. f′/f=lnx+1f'/f = \ln x + 1f′/f=lnx+1. f′(x)=xx(lnx+1)f'(x) = x^x(\ln x + 1)f′(x)=xx(lnx+1). f′(1)=1⋅(0+1)=1f'(1) = 1 \cdot (0+1) = 1f′(1)=1⋅(0+1)=1.
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