Derivative of 1/x^n: Simplifying the Process

[mbrmbrg]

If you want to take the derivative of \frac{1}{x^n} do you turn it into x^-n and go from there or somhow use the fact that the anti derivative of 1/x is ln x?

 

[HallsofIvy]

The fact that "the anti derivative of 1/x is ln x" is irrelevant to the anti-derivative of \frac{1}{x^n}. Write as x^-n. Because \frac{1}{x^n}= x^{-n}, the anti-derivative of 1 is the anti-derivative of the other.

 

[mbrmbrg]

Thanks!