How to solve this function using the product rule?
i understand how the product rule works but when there is cosine and sin, i get quite confused.
could you explain step by step on how to approach this problem?
you

The product rule:







differentiating, using the prime symbol to assume differentiation with respect to x:



the sum/difference rules says we can differentiate each term separately and add them up.





focusing on  :



derivative  of cosine x (with respect to x)  is negative sine x.
derivative of x (with respect to x) is 1.





focusing on :



derivative of sine x (wrt x) is cosine x.
derivative of  (wrt x) is  .







bringing these results together:



you can leave your answer as is, or move all the sine terms together and cosine terms together to factor them out: