 Hello friends welcome to the session I am Malka I am going to help you solve the problem that is differentiate with respect to x the function in exercises 1 to 11 our question is y makes to the power 3 cos 2x. Now let us start with the solution let us suppose that y equal to 5x to the power 3 cos 2x. Now we will take the log on both the sides taking log both sides we get log y equal to 3 cos 2x into log 5x. Now we will differentiate both sides with respect to x differentiate both sides with respect to x we get 1 upon y into dy by dx equal to how we apply the product rule here we get first term into differentiation of second term that is dy dx of log 5x plus second term into dy dx of first term that is 3 cos 2x this implies 1 upon y dy by dx equal to 3 cos 2x into differentiation of log 5x is 1 upon 5x into 5 plus log 5x into dy dx of 3 cos 2x is 3 into minus sin 2x into 2 this implies 1 upon y dy by dx equal to 5 5 cancel out 3 cos 2x upon x plus log 5x into minus 6 sin 2x this implies dy by dx equal to y into 3 cos 2x upon x minus 6 sin 2x log 5x therefore dy by dx equal to now we will substitute the value of y which is 5x to the power 3 cos 2x into 3 cos 2x upon x minus 6 sin 2x log 5x so this is the required solution hope you understood it and enjoyed the session goodbye and take care