Question

if y= log x / x show that d^2y/dy^2= 2 log x-3/x^3

Answer 1

y=logxxDifferentiating both side w.r.t x, we have,dydx=ddxlogxx=xddxlogx-logxddxxx2=x1x-logxx2=1-logxx2Again differentiating w.r.t.x, we have,d2ydx2=ddx1-logxx2=x2ddx1-logx-1-logxddxx2x4=x2-1x-1-logx2xx4=-x-2x+2xlogxx4=2logx-3x3⇒d2ydx2=2logx-3x3

Answer 2

pl. see attachment for the proof
we have to differentiate two times