How do you differentiate #f(x)= (3x+1)^4(2x-3)^3 # using the product rule?
Now, we just plug in everything:
The problem arises at the fact that your two functions are actually compositions of functions. For example,
So first, we do the outermost function (in this case
Now, for the second one:
Again, same process. Derivative of the outside, then multiply by derivative of the inside:
We're done! Now, we just go ahead and plug these back into the product rule equation we got for our final answer:
You could foil out some stuff here, but in my opinion, it's really just more work. Easier to leave it as is.
Hope that helped :)