Question

Find the second derivative of log x

Answer 1

$DIFFERENTIATION \\ \\ \\ Let \: \: y \: = \: log(x) \\ \\ \frac{dy}{dx} \: = \: \frac{1}{x} \\ \\ For \: second \: derivative \: , \: taking \: the \\\: expression's \: derivation \: \: again \\ \: \: \: w.r.t \: \: \: x \\ \\ \frac{ {d}^{2}y }{d {x}^{2} } = \frac{d( \frac{1}{x}) }{dx} \\ \\ \\ \frac{ {d}^{2}y }{d {x}^{2} } = \: \frac{ - 1}{ {x}^{2} } \: \: \: \: \: \: \: \: \: \: \: \: Ans.$