Answer:
Step-by-step explanation:
Let's first subtitute [tex]e^{7xcosx}[/tex] with [tex]g(x)[/tex]
This will turn the problem into
[tex]y = e^{g(x)}[/tex]
Using the chain rule, we will find that the derivative of this function, [tex]y'[/tex], is represented by the following:
[tex]y' = g'(x)e^{g(x)}[/tex]
We know what [tex]g(x)[/tex] is in this case, but we need to find [tex]g'(x)[/tex].
This can be done with the product rule:
[tex]g'(x) = 7cos(x) - 7xsin(x)[/tex]
Plugging these functions back into the original subtitution will give you the final answer:
[tex]y' = (7cos(x) - 7xsin(x))e^{7xcosx}[/tex]
