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Differentiate with respect to `x`:
`e^(tan(2x))` (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`2 sec^2(2x)* e^(tan(2x))`
| `y` | `=e^(tan(2x))` |
| `dy/dx` | `= d/(dx)tan(2x) xx e^(tan(2x))` |
| `= 2 sec^2(2x)* e^(tan(2x))` |
Differentiate with respect to `x`:
`(1 + tan x)^10`. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
`10 sec^2 x \ (1 + tan x)^9`
`y = (1 + tan x)^10`
| `(dy)/(dx)` | `= 10 (1 + tan x)^9 xx d/(dx) (1+tan x)` |
| `= 10 sec^2 x \ (1 + tan x)^9` |
Differentiate `x tan x` with respect to `x`. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
`dy/dx = x sec^2 x + tan x `
`y = x tan x`
`text(Using product rule)`
| `d/dx (uv)` | `=uv ^{prime}+ u^{prime}v` |
| `:.dy/dx` | `=x xx sec^2 x+ 1 xxtan x ` |
| `= x sec^2 x + tan x` |
Differentiate `x^2 tan x` with respect to `x`. (2 marks)
--- 3 WORK AREA LINES (style=lined) ---
`2x tanx + x^2 sec^2 x`
`y = x^2 tan x`
`text(Using product rule:)`
| `d/dx (uv)` | ` = u^{prime} v + u v^{prime}` |
| `dy/dx` | `=2x tanx + x^2 sec^2 x` |