The process of identifying the nth derivative is essentially about performing differentiation on a function n times. Each successive derivative gives us a deeper understanding of change rates, such as speed and acceleration. Often, the nth derivative is denoted as f^n(x) or D^n[f(x)] and involves the recurrent use of rules for differentiation.
| Topic | Problem | Solution |
|---|---|---|
| None | Find the second derivative of the function. 6) $s… | Given the function \(s=\frac{t^{8}+9 t+8}{t^{2}}\), we are asked to find the second derivative. |
| None | Find $y^{\prime \prime}$ if $y=4 \sec x$ | We are given the function \(y = 4 \sec x\). We need to find the second derivative of this function. |