Differentiate (4x-2)^5(1-x^3)^5?

y = (4x-2)^5(1-x^3)^5
y = -1024x^20 + 2560x^19 - 2560x^18 + 6400x^17 - 13120x^16 + 12832x^15 - 16640x^14 + 27200x^13 - 25760x^12 + 23040x^11 - 28800x^10 + 25920x^9 - 17920x^8 + 16000x^7 - 13120x^6 + 7424x^5 - 4160x^4 + 2720x^3 - 1280x^2 + 320x - 32
y' = -20480x^19 + 48640x^18 - 46080x^17 + 108800x^16 - 209920x^15 + 192480x^14 - 232960x^13 + 353600x^12 - 309120x^11 + 253440x^10 - 288000x^9 + 233280x^8 - 143360x^7 + 112000x^6 - 78720x^5 + 185600x^4 - 16640x^3 + 8160x^3 - 2560x + 320...Show more

use product rule and chain rule
let y'=uv'+vu'
u=(4x-2)^5, u'=5(4x-2)^4(4x), u'=20x(4x-2)^4
v=(1-x^3)^5, v'=5(1-x^3)^4(-3x^2), v'=-15x^2(1-x^3)^4
plug in the values
y'=(4x-2)^5[-15x^2(1-x^3)^4]+ (1-x^3)^5[20x(4x-2)^4]
Answer: y'=(4x-2)^5[-15x^2(1-x^3)^4]+ (1-x^3)^5[20x(4x-2)^4]...Show more