Hans Georg Schaathun
September 2016
| \(\int f(x)dx\) | \( f(x)\) | \( f'(x)\) |
|---|---|---|
| \(\vdots\) | \(\vdots\) | \(\vdots\) |
| \(\frac14x^4\) | \(x^3\) | \(3x^2\) |
| \(\frac13x^3\) | \(x^2\) | \(2x\) |
| \(\frac12x^2\) | \(x\) | \(1\) |
| \(x\) | \(1=x^0\) | \(0\) |
| \( ??? \) | \(\frac1x=x^{-1}\) | \(-\frac1{x^2}\) |
| \( -\frac1x \) | \(\frac1{x^2}\) | \(-2\frac1{x^3}\) |
| \( -\frac1{2x^2} \) | \(\frac1{x^3}\) | \(-3\frac1{x^4}\) |
| \( -\frac1{3x^3} \) | \(\frac1{x^4}\) | \(-4\frac1{x^5}\) |
| \(\vdots\) | \(\vdots\) | \(\vdots\) |
$$f(x) = \frac1x$$
$$\ln x $$
| \(\ln 1 = 0\) |
| \(\ln (xy) = \ln x + \ln y\) |
| \(\ln \frac1x = - \ln x \) |
| \(\ln \frac xy = \ln x - \ln y \) |
| \(\ln (x^y) = y\ln x\) |