How do you find the derivative of $f (x) = {log}_{x} e$ $f(x) = log_x e$ ?

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Answer 1 · 2016-04-10T20:57:23

Use change of base to write $f (x) = \frac{ln e}{ln x} = \frac{1}{ln x} = {(ln x)}^{- 1}$ $f(x) = lne/lnx = 1/lnx = (lnx)^-1$

So $f'(x) = -(lnx)^-2 (1/x) = (-1)/(xln^2x)$

How do you find the derivative of f(x) = log_x ef(x)=logxef(x) = log_x e?