Calc2.64

From Example Problems
Revision as of 01:23, 27 November 2007 by Scottie 000 (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Write y=x^{y}\,
\Rightarrow \ln y=y\ln x\,

\Rightarrow {\frac  {y'}{y}}={\frac  {y}{x}}+y'\ln x

{\frac  {y'}{y}}-y'\ln x={\frac  {y}{x}}

y'\left[{\frac  {1-y\ln x}{y}}\right]={\frac  {y}{x}}

y'={\frac  {y^{2}}{x-xy\ln x}}

f'(x)={\frac  {x^{{2x^{{x^{{{\cdot }^{{{\cdot }^{{\cdot }}}}}}}}}}}{x-x^{{1+x^{{x^{{{\cdot }^{{{\cdot }^{{\cdot }}}}}}}}}}\ln x}}\,