anonymous
  • anonymous
How do you find the second derivative using the definition of the first derivative?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
just derive the first derivative to find the second... y = x^2 y' = 2x y'' = 2
anonymous
  • 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.
anonymous
  • anonymous
Take the derivative of the first derivative. The result will be the second derivative.

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anonymous
  • 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!
anonymous
  • 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)?
anonymous
  • anonymous
\[f'(x) = \lim_{\Delta x \rightarrow 0} [f(x + \Delta x) - f(x)]/\Delta x\] \[\rightarrow \lim_{\Delta x \rightarrow 0} [ f'(x + \Delta x) - f'(x)]/\Delta x = ?\]
anonymous
  • 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.

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