Question

if y= logx/x, show that d2y/dx2=2logx-3/x3

Answer 1

$y = \frac{logx}{x} \\ \\ differentiate \: wrt \: to \: x \: \\ \\ \frac{dy}{dx} = \frac{x. \frac{d( log(x)) }{dx} - log(x). \frac{dx}{dx} }{ {x}^{2} } \\ \frac{dy}{dx} = \frac{1 - logx}{ {x}^{2} } \\ \\ again \: differentiate \: wrt \: x \: \\ \\ \frac{ {d}^{2}y }{d {x}^{2} } = \frac{ {x}^{2} \frac{d(1 - logx)}{dx} - (1 - logx) \frac{d {x}^{2} }{dx} }{ {x}^{4} } \\ \\ \: \: \: \: \: \: \: \: = \frac{ {x}^{2}(0 - \frac{1}{x}) - (1 - logx)2x }{ {x}^{4}} \\ \\ \: \: \: \: \: \: \: = \frac{2xlogx - 3x}{ {x}^{4} } \\ \\ \: \: \: \: \: \: \: = \frac{2logx - 3}{ {x}^{3} }$

Answer 2

Answer:

Step-by-step explanation: