Use the definition of the derivative f'(x)=lim h-0 f(x+h)-f(x)/h to find f'(x) where f(x)=x^2+x

Question

Use the definition of the derivative f'(x)=lim h->0 f(x+h)-f(x)/h to find f'(x) where f(x)=x^2+x

mathmale · Answer

Your function is f(x) = x^2 + x.

Please find $$f(x+ \Delta x)$$

mathmale · Answer

Then write out and simplify the difference quotient, $$\frac{ f(x+ \Delta x)-f(x) }{ \Delta x}$$

mathmale · Answer

Finally, let that delta x go to zero.  The result is your derivative, f '(x).

mathmale · Answer

You can, of course, use "h" instead of "delta x."

canada907cat · Answer

would it be [(x+h)^2+(x+h)]-x^2+x/h?

canada907cat · Answer

would the answer be 2x?

canada907cat · Answer

@mathmale

mathmale · Answer

f '(x) = 2x     plus an integer.  Something got lost in process.  Review your work and see if you can find the missing term for the derivative.

canada907cat · Answer

2x+1 then?

canada907cat · Answer

How can it be 2x+1?

mathmale · Answer

Except for the missing label, your result is fine.  What leads you to believe it's not?

mathmale · Answer

Try using the definition of the derivative to find the derivative of g(x)=x.  Your result?

canada907cat · Answer

I don't know how to compute that but I will take your word for it. Thank you for helping.