Jashan

k-12

student

hi, i am studying differentation at the moment
i have drawn some graphs such as y=x^{ 2}. i have found the formula for
the gradient of this curve, this being 2x obtained by using differentation,
but i need to know the general case for the formula where y=x^{n } in order for me to understand this topic more throughly, i would also
like to know how u derived this general formula

thankyou

Hi Jashan,
Developing an expression for the differentiation of y = x^{ n} is one of the first topics that are usually covered in a beginning calculus course. In my calculus class I begin, as you did, by considering y = x^{ 2}. I am not sure how you arrived at the derivative, but I take the process that I used as an introduction to the concept of a limit. We then spend some time on limits before coming back to y = x^{ 3} and y = x^{ 4} ( as well as y = x^{ 1}). I next develop the sum, difference and product rule for diffetentiation and use the product rule to prove, by mathematical induction, that the derivative of y = x^{ n} is n x^{ n-1} for n a positive integer.

I hope this helps,

Harley