Differentiate y=(2x-3)^4 (6-5x)?

Question

? how do you defferentiate step by step

Answer 1

f `(x) = 4(2 x - 3)³ (2)(6 - 5 x) - (5)(2 x - 3)^4
f `(x) = (2 x - 3)³ (48 - 40 x - 10 x + 15)
f `(x) = (2 x - 3)³ (63 - 50 x)

Answer 2

D[(2x-3)^4 (6-5x)]= [D(2x-3)^4](6-5x) + [D(6-5x)](2x-3)^4;
=4(2x-3)^3 *2 (6-5x) + (-5)(2x-3)^4;
=-320x^4 + 1824x^3 -3888x^2 + 3672x -1296 +(-5) (2x-3)^4;
= -400x^4 + 2304x^3 -4968x^2 +4572x -1701

Answer 3

product rule formula, ( write it out will be clearer )

d(uv) /d x = u * dv / dx + v * du / dx

let y = (6-5x)(2x-3)^4

(6-5x) = u,
(2x-3)^4 = v

so y = uv
----------------------------

y = (6-5x)(2x-3)^4 -------------( applying the above formula )

dy/dx
=(6-5x) * 4(2x-3)^3 * (2) + (2x-3)^4 * (-5)
=(6-5x) * 8(2x-3)^3 - 5(2x-3)^4
=8(6-5x) (2x-3)^2 - 5(2x-3)^4