Can someone please explain this step by step? Find the derivative of x^(2) +3x - 5 using the definition of the derivative (i.e.) using limits. I know the answer is 2x+3 using power rules and the like, but I can't figure out how and where to plug in the numbers using f(x) (x+h)-f(x)/h

Question

Can someone please explain this step by step?  Find the derivative of x^(2) +3x - 5  using the definition of the derivative (i.e.) using limits.  I know the answer is 2x+3 using power rules and the like, but I can't figure out how and where to plug in the numbers using f(x) (x+h)-f(x)/h

anonymous · Answer

$$f(x)=x^2+3x-5$$
$$f(x+h)=(x+h)^2+3(x+h)-5=x^2+2xh+h^2+3x+3h-5$$
$$f(x+h)-f(x)=2xh+h^2+3h$$
$$\frac{f(x+h)-f(x)}{h}=2x+3+h^2$$ now take the limit as h goes to zero (by replacing h by zero) and get 
$$2x+3$$

laddiusmaximus · Answer

ok why is it 2xh?