Question

Hey, I literally just started Calc and when doing the derivatives, I noticed that



http://www.wolframalpha.com/input/?i=derivative+of+x

http://www.wolframalpha.com/input/?i=derivative+of+x%5E2

http://www.wolframalpha.com/input/?i=derivative+of+x%5E3

http://www.wolframalpha.com/input/?i=derivative+of+x%5E4

http://www.wolframalpha.com/input/?i=derivative+of+x%5E5

When you have x raised to a degree n, the derivative is just the degree times x^(n-1), is there a rule for this?

Answer 1

its called a power rule ....

Answer 2

Its nX^(n-1).......and Yes its arule!!

Answer 3

Derived though!!

Answer 4

Oh, thats cool, and I feel smart for figuring that out :)

Answer 5

\[\lim\frac{(x+h)^n-x^n}{h}\]
\[\lim\frac{(x^n+c_ox^{n-1}h+c_1x^{n-2}h^{2}+...+h^n)-x^n}{h}\]
\[\lim\frac{c_ox^{n-1}h+c_1x^{n-2}h^{2}+...+h^n}{h}\]
\[\lim\frac{h(c_ox^{n-1}+c_1x^{n-2}h+...+h^{n-1})}{h}\]
\[\lim ~c_ox^{n-1}+c_1x^{n-2}h+...+h^{n-1}=c_ox^{n-1}\]
the next thing to determine is what the coefficient would be

Answer 6

Oh, ok, thanks both of you

Answer 7

the coeef, from the binomial thrm setup is n choose 1, which is just n :) good luck

Answer 8

YW