Power+Rule

= = = = =  = = = = = ==Definition: If n is a rational number, then the function f(x) = x^n is differentiable as follows:       <span style="FONT-SIZE: 60%; COLOR: rgb(51,51,204); FONT-FAMILY: Wingdings">    == ==<span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)"> == ==<span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Arial,Helvetica,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)">In other words: ==

To find the derivative of x^n, it's the exponent * x^(exponent - 1).
<span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Arial,Helvetica,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)"> ==<span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Arial,Helvetica,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)">Example: ==

f(x) = <span style="COLOR: rgb(221,3,165)">6 x^<span style="COLOR: rgb(7,156,2)">2 Find f '<span style="COLOR: rgb(5,5,5); FONT-FAMILY: Arial,Helvetica,sans-serif"> (x)
==<span style="COLOR: rgb(5,5,5)"> f '(x) = <span style="COLOR: rgb(221,3,165)">6<span style="COLOR: rgb(5,5,5)">•<span style="COLOR: rgb(7,156,2)">2<span style="COLOR: rgb(3,3,3)">x^<span style="COLOR: rgb(7,156,2)">2-1    == ==<span style="COLOR: rgb(221,3,165)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(3,3,3)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(5,5,5)">f '(x) = 12x     == ==<span style="COLOR: rgb(221,3,165)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(3,3,3)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(5,5,5)">     == ==<span style="COLOR: rgb(221,3,165)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(3,3,3)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Arial,Helvetica,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)">Application:       ==

media type="custom" key="641773" ==<span style="COLOR: rgb(221,3,165)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(3,3,3)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Arial,Helvetica,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)"><span style="COLOR: rgb(5,5,5); FONT-FAMILY: Arial,Helvetica,sans-serif">        ==

==<span style="COLOR: rgb(221,3,165)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(3,3,3)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Arial,Helvetica,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)">Links:       <span style="COLOR: rgb(221,3,165)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(3,3,3)"><span style="COLOR: rgb(7,156,2)"><span style="COLOR: rgb(5,5,5)"><span style="COLOR: rgb(9,7,146); FONT-FAMILY: Impact,Charcoal,sans-serif; BACKGROUND-COLOR: rgb(245,142,10)"><span style="COLOR: rgb(13,32,206); FONT-FAMILY: Arial,Helvetica,sans-serif; BACKGROUND-COLOR: rgb(245,120,15)">        ==