What is the derivative of sin(2x)ln(x^2) sin(2x)ln(x2)?

1 Answer
Jan 3, 2016

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)