Recall that if we have y = f(g(x)) that
And if y = f(g(h(x)))
So to facilitate this process a bit I'm going to rewrite this as:
We are going to be using the product rule: y = f(x)g(x) --> y' = f'(x)g(x) + f(x)g'(x). Then we use the chain rule on the individual factors.
After a bit of simplifying I get:
Now. At the point (2, 4) the slope has a value of -93/2. Thus the tangent line will be:
and will pass through the point (2, 4):
Thus the tangent line is