How do you differentiate # y =sin(ln(cos x)) # using the chain rule?

1 Answer
Jan 15, 2016

Answer:

#dy/dx = - cos (ln(cosx)) . tanx #

Explanation:

Differentiate using the 'chain rule' :

#dy/dx = cos(ln(cosx)) .d/dx (ln(cosx)) #

#dy/dx = cos(ln(cosx)).( 1/cosx . d/dx(cosx)) #

#dy/dx = cos(ln(cosx)) . (1/cosx .(- sinx)) #

#dy/dx = cos(ln(cosx)) . (- sinx/cosx ) #

#rArr dy/dx = - cos(ln(cosx)). tanx #