i understand we need to use the chain method here but isnt p

i understand we need to use the chain method here. but isnt product rule also in effect? can someone tell me in steps how to solve this? id think youd do sec^2 and then use the product rule for dir. of cos times dir of 5? sec^2 ( cos X 5 ) + ( -sin X 5x) ?

please dont just give the answer. i need to know how this is done. what terms are used in the product rule. why?

Solution

Derivative of tan(cos(5*x)) by x : -5*sin(5*x)*sec(cos(5*x))^2