How do you differentiate #y = 1/2 x + 1/4sin2x#?
1 Answer
Dec 20, 2016
Explanation:
This can be rewritten as follows using the identity
#y = 1/2x + 1/4(2sinxcosx)#
#y = 1/2x + 1/2sinxcosx#
#y = 1/2(x + sinxcosx)#
#2y = x + sinxcosx#
Use implicit differentiation and the product rule to differentiate.
#2(dy/dx) = 1 + cosx(cosx) + sinx(-sinx)#
#2(dy/dx) = 1 + cos^2x - sin^2x#
Use the identity
#2(dy/dx) = cos^2x + cos^2x#
#2(dy/dx) = 2cos^2x#
#dy/dx = (2cos^2x)/2#
#dy/dx= cos^2x#
Hopefully this helps!