If #f(x)= cos(-2 x -1) # and #g(x) = 3x^2 -5 #, how do you differentiate #f(g(x)) # using the chain rule?
The chain rule says that the derivative of a compound function like
or, the derivative of the whole thing is the derivative of the inside times by the derivative of the outside (with the inside left the same).
The question gives us the functions, so differentiate them normally, like so
We can put these functions into the chain rule equation,