On clip 4 of this link: http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/part-a-definition-and-basic-rules/session-2-examples-of-derivatives/
the teacher explains how he uses the binomial theorem to substitute for (x+dx)^n. What I don't get is: how did he simplify the binomial theorem down to x^n + (nx^(n-1))dx?
In other words, I don't understand how he simplified the binomial theorem in the video at around 46:30.

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\[x^n + nx^{n-1}\Delta x \] is the problem I wrote in my post.

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