In order to do derivatives, you need to be on point with algebraic principles and then the derivative rules. For example, the power rule can get confusing if you see a function that has a 7th root like in the first problem. But if you recognize that it's the same thing as x to the 1/7th power you can apply the power rule much easier. And for variables with exponents in the denominator don't make your life miserable and do quotient rule when you can simply move it to the numerator with a negative exponent. So 1 over x to the 7th becomes x to the negative 7.