How do you differentiate #y = (x + 7)^10 (x^2 + 2)^7#?
Use the product rule, and the power and chain rules.
In this case
With practice, it will not be necessary to write all of the above.
We've finished the calculus, but we can clear up the answer using algebra:
We really have two terms (Things that are added are called "terms".)
Usually, we'll clean up both terms, but the first term here is fine, so we'll just clean up the second.
Notice the common factors. Let's factor them out:
Now we can finish by simplifying the expression in the square brackets.
You can change those square brackets to parentheses and move that factor to right after the