Question

Question #dbf21

Answer 1

`(dy)/(dx) = 2/x`

Explanation:

Starting with the equation:

`y=ln(3x^2)`

We wish to find the derivative. To do so, we must apply the chain rule:

`(dy)/(dx)=d/(dx) ln(3x^2) = d/(dv) ln(v) * d/(dx)v`

where `v=3x^2`. We know that:

`d/(dv) ln(v) = 1/v = 1/(3x^2)`

and:

`d/(dx)v=d/(dx) (3x^2) = 3*d/(dx) x^2 = 3*2*x = 6x`

Putting it together we get:

`(dy)/(dx) = (6x)/(3x^2) = 2/x`

Answer 2

`2/x`

Explanation:

Using the chain rule:

`:.`

`dy/dx=dy/(du)*(du)/(dx)`

Let `u = 3x^2`

`dy/dxln(u)=dy/(du)ln(u)*(du)/dx(u)=1/u*6x=1/(3x^2)*6x=color(blue)(2/x)`