Calculus
Differentiation Using The Chain Rule
Applied To Log Functions Of Type y = c(lnx)n
where c is a constant
y = c(ln x)n
dy/dx = n × c(ln x)n-1(differential of ln x)
[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 = 3(ln x)5 with respect to x | ||||||||||
| [1] 'Differentiate with respect to the brackets' | dy/d(...) = (5)3(ln x)4 | |||||||||
| [2] Multiply by the 'inside differential' | dy/dx = (5)3(ln x)4(1/x) | |||||||||
| [3] Simplify |
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A presentation that shows the method and works to avoid error is
y = 3(ln x)5
dy/dx = (5)3(ln x)4(1/x)
| dy | 15(ln x)4 | |
| = | ||
| dx | x |
