## anonymous 5 years ago How do you find the second derivative using the definition of the first derivative?

1. amistre64

just derive the first derivative to find the second... y = x^2 y' = 2x y'' = 2

2. anonymous

I am not given an a y= equation. I am given the definition of the first derivative and asked to find the derivative of the second derivative of the second using the first derivative equation only.

3. anonymous

Take the derivative of the first derivative. The result will be the second derivative.

4. anonymous

When taking a derivative, you decrease the power of the exponent by 1 while increasing the coefficient by one. For example, if you have y = x^2, you decrease the power to 1 and increase the coefficient to 2 so y'=derivative of y = 2x. Repeat this process to determine the second derivative. y" = second derivative of y = first derivative of y' = 2. Good luck!

5. anonymous

yes I know that, but how do i specifically take the derivative of the equation: f(x+deltax)-f(x)/deltax as the lim of delta x goes to infinity (the definition of the first derivative)?

6. anonymous

$f'(x) = \lim_{\Delta x \rightarrow 0} [f(x + \Delta x) - f(x)]/\Delta x$ $\rightarrow \lim_{\Delta x \rightarrow 0} [ f'(x + \Delta x) - f'(x)]/\Delta x = ?$

7. anonymous

The result of that second expression should be f''(x). Just plug in x+Delta_x as x into f' to get the first term, and just x as your input for f' to get the second term, then divide both by another Delta_x.