Question

What is the derivative of `sin(2x)ln(x^2)`?

Answer 1

We have a product of two terms that will demand chain rule.

Explanation:

• Product rule: `(ab)'=a'b+ab'`
• Chain rule: `(dy)/(dx)=(dy)/(du)(du)/(dx)`

Renaming `u=2x` and `v=x^2` so that we can differentiate these terms.

`(dy)/(dx)=2cos(2x)(ln(x^2))+2cancel(x)sin(2x)(1/x^cancel(2))`

`(dy)/(dx)=2(cos(2x)ln(x^2)+sin(2x)/x)`