Question
Differentiate the following from first principle:
$-\text{x}$
$-\text{x}$
$\therefore\frac{\text{d}}{\text{dx}}\Big(\text{f}(\text{x})\Big)=\lim_\limits{\text{h}\rightarrow0}\frac{\text{f}(\text{x}+\text{h})-\text{f}(\text{x})}{\text{h}}$
$\Rightarrow\frac{\text{d}}{\text{dx}}\Big(\text{f}(\text{x})\Big)=\lim_\limits{\text{h}\rightarrow0}\frac{-(\text{x}+\text{h})+(\text{x})}{\text{h}}$
$\Rightarrow\frac{\text{d}}{\text{dx}}\Big(\text{f}(\text{x})\Big)=\lim_\limits{\text{h}\rightarrow0}\frac{-\text{h}}{\text{h}}$
$\Rightarrow\frac{\text{d}}{\text{dx}}\Big(\text{f}(\text{x})\Big)=\lim_\limits{\text{h}\rightarrow0}-1$
$\Rightarrow\frac{\text{d}}{\text{dx}}\Big(\text{f}(\text{x})\Big)=-1$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| Size | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 |
| Frequency | 3 | 3 | 4 | 14 | 7 | 4 | 3 | 4 |
| C1 | | C2 | |
| | Probability | | Written Description. |
| a. | 0.95 | i. | An incorrect assignment. |
| b. | 0.02 | ii. | No chance of happening. |
| c. | -0.3 | iii. | As much chance of happening as not. |
| d. | 0.5 | iv. | Very likely to happen. |
| e. | 0 | v. | Very little chance of happening. |
$\cos\Big(\text{x}-\frac{\pi}{8}\Big)$