Question

What is the derivative of `(2ln(x+3))/x^2`?

Answer 1

answer = `"-2(x+6)"/x^3`

Explanation:

`d/dx(u/v)="u'v-v'u"/v^2`
similarly, `d/dx((2(x+3))/x^2)=d/dx((2x+6)/x^2)`
=`((x^2)d/dx(2x+6)-(2x+6)d/dx(x^2))/(x^2)^2`
=`((x^2)(2)-(2x+6)(2x))/x^4`
=`(2x^2-4x^2-12x)/x^4`
`(-2x^2-12x)/x^4`
`(-2x(x+6))/x^4=(-2(x+6))/x^3`