Differentiate the following expressions with the help of the power rule:
| `x^2 + 2x - 1` | `2x + 2` | |
| `3x^5 - 1/2x^4 + 6x^2 - 5` | `2/x^5+15 x^4+12 x` | |
| `3sqrt{t} + 2cbrt{t}` | `(3/2)t^(-1/2) + (2/3)t^(-2/3)` | |
| `1/{sqrt(x)} + x^{10/3}` | `(-1/2)x^(-3/2) + (10/3)x^(7/3)` | |
| `2x^-2 + x^-1 + 3x` | `-4x^-3 - x^-2 + 3` | |
| `10/x^2 + 1/x - 1/{sqrt{x}}` | `-20x^-3 - x^-2 + 1/2x^(-3/2)` | |
| To which of the following can the power rule not be applied? a)`e^x` b) `x` c) `1^x` d) `x^x` | A and D because these contain variables as exponents. C is simplified as `1^x = 1` so it doesn't have a variable in its exponent. | |
| `x^-5/{sqrt{x}} + 1/x^2` | `-11/2x^(-13/2) - 2x^(-3)` | |
| `x^n + 1/x^n` | `nx^(n-1) - nx^(-n-1)` | |
| `5x^10/{sqrt{x}} - (1/10)x^(-12)` `+ 5/(6x^(-1/5)) + 2x^3/{cbrt{x}}` | `95/2x^(17/2) + 6/5x^(-13) + 1/6x^(-4/5) + 16/3x^(5/3)` |
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