Differentiate xcos2x. derivative of xcos2x is =?
- print Print
- list Cite
Expert Answers
Tushar Chandra
| Certified Educator
calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
We have to differentiate f(x) = x*cos 2x
f'(x) = x'*cos 2x + x*(cos 2x)'
f'(x) = cos 2x + x*(-sin 2x)*2
f'(x) = cos 2x - 2x*(sin 2x)
The required derivative of f(x) = x*cos 2x is f'(x) = cos 2x - 2x*(sin 2x)
giorgiana1976 | Student
Let y = x*cos2x
We'll apply the chain rule and also the product rule.
dy/dx = [d/dx(x)]* cos2x + x* [d/dx (cos 2x)]
We'll apply the chain rule for the term:
[d/dx (cos 2x)] = -sin 2x* (2x)'
[d/dx (cos 2x)] = -2sin 2x
The differentiated given function is: dy/dx = cos 2x - 2x(sin 2x)
Student Answers