At this point we will only prove this theorem for values of {{MATH_56}} which are positive integers. Later we will give the complete explanation. From the limit definition of the derivative, write with me {{MATH_57}} Expand the term {{MATH_58}}: {{CMD_59}} {{ENV_60}} {{CMD_61}} Note that we are using the Binomial Theorem to write {{MATH_62}} for the coefficients. Canceling the terms {{MATH_63}} and {{MATH_64}}, and noting {{MATH_65}}, write with me {{CMD_66}}{{ENV_67}}{{CMD_68}} since every term but the first has a factor of {{MATH_69}}. Therefore, {{MATH_70}} {{CMD_71}} {{CMD_72}}