What do you get when you apply the two-point forward finite difference formula for the first derivative of $f(x)$ to the two-point forward finite difference formula for the first derivative of $f(x)$?
2026-03-28 17:05:40.1774717540
Applying two-point forward to two-point forward formula
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The two-point forward finite difference formula for the first derivative of $f(x)$ at $x_0$ is given by the expression
$$\frac{f(x_0 + h) - f(x_0)}{h}.$$
Recall that this is an approximation of $f'(x_0)$:
$$f'(x_0) \approx \frac{f(x_0 + h) - f(x_0)}{h}.$$
If you apply this formula to the first derivative of $f$, the resulting expression is
$$\frac{f'(x_0 + h) - f'(x_0)}{h}.$$
From earlier, we know that this should be an approximation of the first derivative of $f'$ at the point $x_0$.
What is the first derivative of $f'$?