2007-09-20 06:21:25 · 6 answers · asked by justblaze322 1 in Science & Mathematics ➔ Mathematics
yes
2007-09-20 06:24:18 · answer #1 · answered by Anonymous · 0⤊ 2⤋
dy/dx = 3*4(5x - 4)^3 * 5 + 6*(-2)/x^3 =
= 60(5x - 4)^3 - 12/x^3
2007-09-20 13:27:27 · answer #2 · answered by Amit Y 5 · 0⤊ 0⤋
y = 3(5x-4)^4+6/x^2 = 3(5x-4)^4+6x^(-2)
dy/dx
=3*4[(5x-4)^3]*5+6(-2)x^(-3)
= 60(5x-4)^3 -12x^(-3)
or dy/dx= 60(5x-4)^3 -12/x^3
2007-09-20 13:33:15 · answer #3 · answered by Debidas M 2 · 0⤊ 0⤋
the rules to differentiate a quotient:
http://people.hofstra.edu/Stefan_Waner/realworld/Calcsumm4.html
you also need the rules to differentiate a a polynomial raised to a power such as....
3(5x-4)^4+6
let y = 5x - 4 you have....
3(y)^4+6
to differentiate that reduce the power on y by 1 and multiply that power by the coiffecient on 3y^4...
3(4)y^3 = 12y^3....
now replace y with 5x - 4 and differnitate it...
12(5x - 4)^3 (5)
now differentiate + 6 ... when a differntiate a constant u get 0..
your final answer is... 60(5x - 4)^3
now follow the rules of differentiating a qoutient with the rules we just discussed to solve...
3(4)(5x - 4)^4 (5) (x^2) - (3(5x - 4)^4 + 6)) (2x)
---------------------------------------------------------
((x^2)^2)
simplify....
60(x^2)(5x-4)^4 - 6x(5x-4)^4 + 12x
----------------------------------------------
x^4
simplify further...
divide out an x...
60x(5x-4)^4 - 6(5x-4)^4 + 12
----------------------------------------------
x^3
2007-09-20 13:38:06 · answer #4 · answered by googooslide2000 3 · 0⤊ 0⤋
dy/dx = (3)(4)(5x-4)^3(5) - ((2x)(6))/x^4
=60(5x-4)^3 - 12/x^3
2007-09-20 13:31:49 · answer #5 · answered by nj 2 · 0⤊ 0⤋
This morning, I've decided to let MAPLE solve all my problems for me. So, MAPLE, take the derivative.
>> maple('diff(3*(5*x - 4)^4 + 6/(x^2),x)')
ans =
60*(5*x-4)^3-12/x^3
Thanks, MAPLE. Ten points for you, good pal.
2007-09-20 13:26:29 · answer #6 · answered by PMP 5 · 0⤊ 0⤋