How do you differentiate #p(y) = y^2sin(y)# using the product rule?

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Answer 1 · 2015-12-01T16:14:48

#p'(y)=2ysin(y)+y^2cos(y)#

According to the product rule:

#p'(y)=sin(y)d/dy[y^2]+y^2d/dy[sin(y)]#

Find each derivative separately.

#d/dy[y^2]=2y#

#d/dy[sin(y)]=cos(y)#

Plug them back in:

#p'(y)=2ysin(y)+y^2cos(y)#

If you want to factor:

#p'(y)=y(2sin(y)+ycos(y))#