What is the derivative of ln(sin(x^2+4))

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The derivative of `ln(sin(x^2 + 4))` has to be determined. Use the chain rule. The derivative is:

`(ln(sin(x^2 + 4)))'*(sin(x^2 + 4))'*(x^2 + 4)'`

=> `1/(sin(x^2 + 4))*cos(x^2 + 4)*2x`

=> `2x*(cos(x^2+4)/(sin(x^2+4)))`

=> `2x*cot(x^2 + 4)`

The derivative of `ln(sin(x^2 + 4))` is `2x*cot(x^2 + 4)`

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial