Question

use the limit derivative to calculate the derivative of y= xsquared + x

Answer 1

Do you know the definition of limit?

Answer 2

For
\[y=x^2+x\]
Let \(y=f(x)\),
\[f(x)=x^2+x\]
Then the definition of limits for derivative is
\[\large f'(x)=\lim_{\Delta x \rightarrow 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}\]
Substitue in f(x), we've got
\[\large f'(x)=\lim_{\Delta x \rightarrow 0}\frac{[(x+\Delta x)^2+x+\Delta x]-(x^2+x)}{\Delta x}\]
Expand and evaluate limit

Answer 3

thats the equation to obtain the limit?

Answer 4

yep