 Hi and welcome to the session I am Deepika here. Let's discuss the question differentiate the following function with respect to x cos x into cos 2x into cos 3x. So let's start the solution. Let y is equal to cos x into cos 2x into cos 3x taking logarithm on both the sides we have we get log y is equal to now we know that log of m into m into p is equal to log m plus log n plus log p therefore log of cos x into cos 2x into cos 3x is equal to log cos x plus log cos 2x plus log cos 3x. Now differentiate both the sides with respect to x 1 by y into derivative of y with respect to x that is dy by dx is equal to 1 over cos x into dy dx of cos x 1 over cos 2x into dy dx of cos 2x plus 1 over cos 3x into dy dx of cos 3x and this is equal to 1 over y into dy by dx is equal to now derivative of cos x is minus sin x therefore this is minus sin x upon cos x minus derivative of cos 2x is minus 2 sin 2x upon cos 2x again derivative of cos 3x is minus 3 sin 3x upon cos 3x so this is equal to minus tan x minus 2 tan 2x minus 3 tan 3x therefore dy by dx is equal to y into minus tan x minus 2 tan 2x minus 3 tan 3x substitute the value of y here we get get dy by dx is equal to minus cos x into cos 2x into cos 3x we have taken minus common into tan x plus 2 tan 2x plus 3 tan 3x hence the answer for the above question is that is the derivative of cos x into cos 2x into cos 3x is minus cos x into cos 2x into cos 3x into tan x plus 2 tan 2x plus 3 tan 3x so this is the answer for the above question I hope the question is clear to you bye and take care