quotient difference

[kahkah]

Given
f(x)=x^2+2x+3
a) Find the difference quotient
(f(x+h)-f(x))/h
b) Use the definitional formula given below to find the derivative ofthe function.

f^' (x)=lim┬(h→0)⁡〖(f(x+h)-f(x))/h〗

 

[kahkah]

let me check

I think this is it:
([(x+h)^2+2(x+h)+3]-[x^2+2x+3])/h

am I correct

 

[pappus]

I think this is it:
([(x+h)^2+2(x+h)+3]-[x^2+2x+3])/h

am I correct<--- yes

The next steps are:

1. Expand the brackets and collect like terms in the numerator. There should be left only terms containing the factor h.

2. Factor out h in the numerator.

3. Cancel h.

4. You have now a sum of terms, some containing h and others don't. If h approaches zero what would happen to those terms containing h?

5. That's it!