How do you differentiate $y=lnx/x^20$ ?

Question

1826 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-31T17:52:06

$dy/dx=(x^19-20x^19 ln x)/x^40$

$y=lnx/x^20$

Use quotient rule $(f/g)^' = (gf'-fg')/g^2$

$f=ln x, g= x^20$

$f'=1/x, g'=20x^19$

$dy/dx=(gf'-fg')/g^2$

$dy/dx=(x^20*1/x-lnx *20x^19)/(x^20)^2$

$dy/dx=(x^19-20x^19 ln x)/x^40$

How do you differentiate y=lnx/x^20y=lnx/x^20?