2.Find the following derivative without simplifying first. Use the quotient rule

Question

2.Find the following derivative without simplifying first. Use the quotient rule on the expressions as written, and then check the answer by simplifying the original expression and then taking the derivative of that simplified expression.

* These are both practice problems that I have gotten stuck with and the explanations that the teacher gives me is in a way that I do not understand. So please show me all work and steps with an explanation so that I am able to know how to do the other problems that are similar to these!

Explanation / Answer

Thanks. For this question, we use the quotient rule, and get

d/dx(x^6/x^2)

= [(x^6)'(x^2) - (x^6)(x^2)'] /(x^2)^2

=[(6x^5)(x^2) - (x^6)(2x)]/ (x^4)

=(4x^7)/(x^4)

=4x^3

Indeed, we can simplify the function (x^6)/x^2)=x^4. We know that (x^4)' = 4x^3 by the derivative of a power function (x^r)=rx^(r-1).

They are the same!!

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