Derivative, Urgent pls

2011-12-19 2:23 am
Find derivative of the following

z(x) = (e^3x)(2x-5)(3x+1)^4
Hints, 要用log

Ans:(e^3x)(3x+1)^3(18x^2-9x-73)

計左成日刀唔識
Thank you all.
更新1:

Thanks much! I made a mistake on step 2 to step 3.

回答 (1)

2011-12-19 2:30 am
✔ 最佳答案
z(x) = (e^3x)(2x - 5)(3x + 1)^4

ln z(x) = 3x + ln(2x - 5) + 4ln(3x + 1)

z'(x)/z(x) = 3 + 2/(2x - 5) + 12/(3x + 1)

z'(x)/z(x) = [3(2x - 5)(3x + 1) + 2(3x + 1) + 12(2x - 5)]/(2x - 5)(3x + 1)

z'(x)/z(x) = [18x^2 - 39x - 15 + 6x + 2 + 24x - 60]/(2x - 5)(3x + 1)

z'(x)/z(x) = (18x^2 - 9x - 73)/(2x - 5)(3x + 1)

z'(x) = z(x)(18x^2 - 9x - 73)/(2x - 5)(3x + 1)

z'(x) = (e^3x)(3x + 1)^3(18x^2 - 9x - 73)





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