Find y' ?? Help

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1 Answer
Cesareo R.
Feb 12, 2018

See below.

Explanation:

Assuming #4x+y > 0# we have

#f(x,y(x))=ln(4x+y(x))-cos(y(x))=0# then

#(df)/(dx) = (4+y'(x))/(4x+y(x))+y'(x) sin(y(x))=0# and now solving for #y'(x)# we have

#y'(x) = -4/((4x+y)siny+1)#

This equation for #y'(x)# have a companion equation which is

#ln(4x+y(x))-cos(y(x))=0#

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