Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

How do you find the derivative of #y=2cosxsinx#

1 Answer

Feb 25, 2015

#2cos(2x)#

Explanation:

Since #y = 2 cos(x) sin(x)# is the same as
#y = sin (2x)#

and
#(d sin(theta))/(d theta) = cos( theta)#

Let #g(a) = sin(a)# and #h(b) = 2b#
(So #y = g(h(x))#)

By the chain rule:
#(d y)/(dx) = (d g(h(x)))/(d h(x)) * (d h(x))/(dx)#

#color(white)((dy)(dx))=(d(sin(2x)))/(d(2x)) * (d(2x))/(dx)#

#color(white)((dy)(dx))= cos(2x) * 2#
or
#color(white)((dy)(dx))= 2 cos(2x)#

Related questions

See all questions in Product Rule

Impact of this question

17952 views around the world

You can reuse this answer
Creative Commons License