Calculus
Differentiation Using The Chain Rule
Applied To Log Functions Of Type y = ln(kx + c)
where c and k are constants
y = ln(kx + c)
dy/dx = [1/(kx + c)] × [differential of (kx + c)]
[1] Differentiate with respect to the brackets as a unit
[2] Multiply by the differential of the inside of the brackets
[3] Simplify
| EXAMPLE | ||||||||||||||||
| Differentiate y = ln(5x + 9) with respect to x | ||||||||||||||||
| [1] 'Differentiate with respect to the brackets' |
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| [2] Multiply by the 'inside differential' |
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| [3] Simplify |
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A presentation that shows the method and works to avoid error is
y = ln(5x + 9)
| dy | 1 | 5 | ||
| = | × | |||
| dx | 5x + 9 |
| dy | 1 | 5 | ||
| = | × | |||
| dx | (5x + 9) | 1 |
| dy | 5 | |
| = | ||
| dx | 5x + 9 |
