Question #11a51

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Answer 1 · 2017-03-08T11:03:52

#y = pi/4-x/2#

#dy/dx = -1/2#

We could determine #dy/dx# using implicit differentiation, but we can also note that:

#cos(x+2y) = 0 => (x+2y) = pi/2+kpi# with #k in ZZ#

and then:

#y= 1/2(pi/2 +kpi-x)#

So whatever is the value of #k#:

#dy/dx = -1/2#

We can then also determine #k# from:

#y(pi/6) = pi/6#

#1/2(pi/2 +kpi-pi/6) = pi/6 #

#pi/2 +kpi-pi/6 = pi/3 => k=0 #

So in conclusion:

#y = pi/4-x/2#

#dy/dx = -1/2#