Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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

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)#

Related questions

See all questions in Differentiating Logarithmic Functions with Base e

Impact of this question

4055 views around the world

You can reuse this answer
Creative Commons License