How do you find the derivative of a function at a certain point?

Answer 1

Well... in order to find the derivative of a function at a certain point... you must learn how to do derivatives. Basic derivatives are simple enough, use these rules to help learn how to do derivatives.... but you want to learn the way how to do them with limits first.. From there, plug in the x value and you will have the derivative at that point..

LIMIT WAY: lim h->0 (f(x+h)-f(x))/h) where f(x) is the beginning function..

Simplified way:

Power rule: n*x^(n-1)
Product rule: vu'+v'u where (v*u)'
Quotient rule: vu'-uv'/v^2 where (u/v)'
Chain rule: n*(x)^(n-1)*(x)' where the begining function is something like (x^2+10x-1)^(1/4)

Answer 2

You find the derivative of the function, and evaluate it at that point.