How do you differentiate #(3x-4/x)^2 (1-x+7x^2)^4#?
Let's work with your function
First, we will rename:
Using the product rule, as follows,
Now, we will lead with the colored derivatives first and then return to the whole equation above.
To solve the green derivative, let's name
The same for the blue part, where
Now we have the derivatives
You may want to expand it and eliminate the factoring (parenthesis), but that is not really necessary as the work and steps to achieve so would not necessarily mean simplification. The line above can be your answer.