How do you find the second derivative using the definition of the first derivative?

Question

amistre64 · Answer

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

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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!

anonymous · Answer

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)?

anonymous · Answer

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

anonymous · Answer

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.