# How do you differentiate #f(x)=cos(3x)*(-2/3sinx)# using the product rule?

##### 1 Answer

#### Answer:

#### Explanation:

Here are some of the rules that need to be used to solve this question:

- Chain rule:
#(df)/dx=(df)/(dg)*(dg)/dx# , where#f# and#g# are functions of#x# - Product rule:
#(d(u*v))/dx=u*(dv)/(dx)+v*(du)/(dx)# , where#u# and#v# are functions of#x# - Constant factor rule (actually a special case of the product rule):
#(d(ku))/dx=k (du)/dx# , where#k# is a constant and u is a function of#x#

First of all, we rewrite the original function to

We shall apply the product rule to find the derivative of

The chain rule is used for finding composite functions. For the chain rule, we say that

Now, we have found

Finally, we apply the constant factor rule, i.e. multiplying this function by