Your idea matters-6

Calculus Level 1

$\large \frac{d}{dx}\ln(x) = ?$

x^{-1}

x^{-\frac{1}{2}}

x^{-2}

\sqrt{x}

1 solution

CodeCrafter 1
Nov 10, 2019

You can prove this by using implicit derivation. $f \left( x \right) = ln \left( x \right) \\ e^{f \left( x \right)} = x$ By deriving it, we get: $e^{f \left( x \right)} \cdot f' \left( x \right) = 1 \\ x \cdot f' \left( x \right) = 1$ Now devide by $x$ and you get:

$\boxed{ f' \left( x \right) = \frac{1}{x} }$

Your idea matters-6

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