How do you differentiate #f(x)=(x-e^x)(cosx+2sinx)# using the product rule?
1 Answer
First you use production rule to get
Then use the linearity of the derivative and function derivative definitions to get
Explanation:
Product rule involves taking the derivative of function which are multiples of two (or more) functions, in the form
Applying it to our function,
We have
Additionally we need to use the linearity of the derivation, that
Applying this we have
We need to do the individual derivatives of these functions, we use
Now we have
At this point we just neaten a bit