Turunan pertama dari y = cos^4 (4x^2- x)

Posted by andi telaumbanua on Feb 13, 2018 in Matematika |
Subscribe

Tentukan turunan pertama dari y = cos^4 (4x^2- x) !

Jawab:

Gunakan aturan rantai

Misalkan: a = (4x^2- x)

maka: da/dx=8x-1

Misalkan: b = cos a

maka: db/da=-sin⁡a = -sin⁡(4x^2- x) 

Sehingga: y = b^4

maka: dy/db=4b^3 = 4(cos a)^3 = 4[cos⁡(4x^2- x)]^3

Maka: dy/db=4 cos^3 (4x^2- x)

Sehingga:

dy/dx = (dy/db)(db/da)(da/dx)

dy/dx = (4 cos^3 (4x^2- x) )(-sin⁡(4x^2- x) )(8x-1)

dy/dx = [8x-1] [-4cos^3 (4x^2- x) sin⁡(4x^2- x)]

dy/dx = [-32x cos^3 (4x^2- x) sin⁡(4x^2- x)] – [-4〖cos〗^3 (4x^2- x) sin⁡(4x^2- x)]

dy/dx = 4cos^3 (4x^2- x) sin⁡(4x^2- x) – 32x cos^3 (4x^2- x) sin⁡(4x^2- x)

for more clear writing please click the link below Tentukan turunan pertama dari y = cos^4 (4x^2- x) !

Reply

Copyright © 2024 All rights reserved. Theme by Laptop Geek.