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Differentiate `pi^(2x)`. (2 marks)
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`2log_e(pi) * pi^(2x)`
| `y` | `=pi^(2x)` |
| `dy/dx` | `=log_e(pi) * 2 * pi^(2x)` |
| `=2log_e(pi) *pi^(2x)` |
Differentiate `5^(x^2)5x`. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
`5^(x^2 + 1)(ln5*2x^2 + 1)`
| `y` | `= 5^(x^2) * 5x` |
| `(dy)/(dx)` | `= ln5*2x*5^(x^2)*5x + 5^(x^2)*5` |
| `=5^(x^2)(ln5*10x^2 + 5)` | |
| `=5^(x^2 + 1)(ln5*2x^2 + 1)` |
Differentiate `3x 6^x`. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`3*6^x(xln6 +1)`
`y= 3x * 6^x`
`text{Using the product rule:}`
`(dy)/(dx)= 3*6^x + ln6 * 6^x *3x= 3*6^x(1 + xln6)`
Differentiate with respect to `x`:
`10^(5x^2-3x)`. (2 marks)
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`(dy)/(dx) = ln 10 (10x-3) * 10^(5x^2-3x)`
`y = 10^(5x^2-3x)`
`(dy)/(dx) = ln 10 (10x-3) * 10^(5x^2-3x)`