3.3: Product and Quotient Rules

The product and quotient rules are both really easy. I actually really don't mind solving derivatives. They're not that bad..

Problem:

1. Find the derivative of ((10x^2 - e^x)(15x + 9^x)) / (5*4th root of x + x^7)
   This problem uses a combination of rules. First apply the quotient rule:
(5*4th root of x + x^7)[(10x^2-e^x)(15x+9^x)]' - (10x^2-e^x)(15x+9^x)(5*4th root of x+x^7)' all divided by (5*4th root of x + x^7)^2.

Then I applied the product rule to find the derivative of [(10x^2-e^x)(15x+9^x)] which is (10x^2-e^x)(15x+9^x)' + (15x+9^x)(10x^2-e^x)'

I also used the power rule to find the derivative where exponents were present. All put together, the derivative of the above function is:
(5*4th root of x + x^7)(10x-e^x)(15+ln9*9^x)+(15x+9^x)(20x-e^x)-(10x^2-e^x)(15x+9^x)((5/4)x^(-3/4)+7x^6) ALL divided by (5*4th root of x + x^7)^2