This is the technique my Prof used to prove the Power Rule for Derivatives. How would I prove it through this technique? / Quote (My Prof): I used the factorization of A^n-B^n=(A-B)(A^{n-1}+A^{n-2}B+A^{n-3}B^2+.... +A B^{n-2}+B^{n-1}). This is the technique my Prof used to prove the Power Rule for Derivatives. How would I prove it through this technique? / Quote (My Prof): I used the factorization of A^n-B^n=(A-B)(A^{n-1}+A^{n-2}B+A^{n-3}B^2+.... +A B^{n-2}+B^{n-1}). @Mathematics

\[\frac{d}{dx} (x^n)=\lim_{x \rightarrow x_0}\frac{f(x)-f(x_0)}{x-x_0}=\lim_{x \rightarrow x_0}\frac{x^n-x_0^n}{x-x_0}\] \[=\lim_{x \rightarrow x_0}\frac{(x-x_0)(x^{n-1}+x^{n-2}x_0+ \cdot \cdot \cdot x x_0^{n-2}+x_0^{n-1})}{x-x_0}\]

What I don't understand is your second line. How does that difference of n's work?

Would you mind explaining as to how you got there with the n's. That is the one part that is confusing to me.

myininaya, what program are you using?

Join our real-time social learning platform and learn together with your friends!