Question

How do you differentiate `f(x)=ln(3x^2)` using the chain rule?

Answer 1

Step by step explanation and working is given below.

Explanation:

`f(x)=ln(3x^2)`

For chain rule, first break the problem into smaller links and find their derivatives. The final answer would be the product of all the derivatives in the link.

`y=ln(u)`
`u=3x^2`

The differentiation using chain rule would be

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

`y=ln(u)`
Differentiate with respect to `u`

`dy/(du) = 1/u`

`u=3x^2`
Differentiate with respect to `x`
`(du)/(dx) = 3(d(x^2))/dx`
`(du)/(dx) = 3*2x`
`(du)/(dx)=6x`

`dy/dx = 1/u*6x`
`dy/dx = (6x)/u`

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

`dy/dx = 2/x` Final answer

Note: The above process might look big, this was given in such a form to help you understand step by step working. With practice, you can do it quickly and with less steps.