Differentiate (3x2 + 2)^4(4 - 5x)^5 and simplify

[yanarains]

Differentiate the given function and simplify your answer

(3x2 + 2)^4(4 - 5x)^5 .

The answer is in the form of

(3x2 + 2)^3(4 - 5x)^4(Ax^2 + 96x - 50) .

Find the value of A.

[4(3x^2+2)^3(6x)](4-5x)^5+(3x^2+2)^4 [5(4-5x)^4(5)]
24x(3x^2+2)^3(4-5x)^5+25(3x^2+2)]

this can be shown as
24A^3B^5 + 25A^4B^4 : then i simplify the answer

A^3B^4 (24B+25A)
=(3x^2+2)^3 (4-5x)^4 [24(4-5x)+25(3x^2+2)]
=(3x^2+2)^3(4-5x)^4[75x^2-120x+146]

This is where I am stuck what do I do next to make my answer look like form given at the top? Of course, I am assuming that my work is correct.

Thanks for the help!

 

[Deleted member 4993]

Differentiate the given function and simplify your answer

(3x2 + 2)^4(4 - 5x)^5 .

The answer is in the form of

(3x2 + 2)^3(4 - 5x)^4(Ax^2 + 96x - 50) .

Find the value of A.

[4(3x^2+2)^3(6x)](4-5x)^5+(3x^2+2)^4 [5(4-5x)^4(-5)].......fix this line

24x(3x^2+2)^3(4-5x)^5+25(3x^2+2)]

this can be shown as
24A^3B^5 + 25A^4B^4 : then i simplify the answer

A^3B^4 (24B+25A)
=(3x^2+2)^3 (4-5x)^4 [24(4-5x)+25(3x^2+2)]
=(3x^2+2)^3(4-5x)^4[75x^2-120x+146]

This is where I am stuck what do I do next to make my answer look like form given at the top? Of course, I am assuming that my work is correct.

Thanks for the help!

 

[yanarains]

OPPS! THANKS BUT I"M STILL A LITTLE STUCK

[4(3x^2+2)^3(6x)](4-5x)^5+(3x^2+2)^4 [5(4-5x)^4(-5)].......fix this line

24x(3x^2+2)^3(4-5x)^5-25(3x^2+2)]

this can be shown as
24A^3B^5 - 25A^4B^4 : then i simplify the answer

A^3B^4 (24B+25A)
=(3x^2+2)^3 (4-5x)^4 [24(4-5x)-25(3x^2+2)]
=(3x^2+2)^3(4-5x)^4[-75x^2-120x+46]

the answer should look like this (3x2 + 2)^3(4 - 5x)^4(Ax^2 + 96x - 50)
I am looking for A: My last two numbers don't match the rest of the answer so A doesn't not =75x^2
what is the next step of this problem in order to make my answer match the answer given?
Hope that makes sense.
Thanks:0

 

[galactus]

\(\displaystyle \L\\(3x^{2}+2)^{4}(4-5x)^{5}\)

Product rule:

\(\displaystyle \L\\(3x^{2}+2)^{4}(5)(4-5x)^{4}(-5)+(4-5x)^{5}(4)(3x^{2}+2)^{3}(6x)\)

\(\displaystyle \L\\-25(3x^{2}+2)^{4}(4-5x)^{4}+24x(4-5x)^{5}(3x^{2}+2)^{3}\)

Factor out:

\(\displaystyle \L\\(4-5x)^{4}(3x^{2}+2)^{3}\left[-25(3x^{2}+2)+24x(4-5x)\right]\)

\(\displaystyle \L\\-(4-5x)^{4}(3x^{2}+2)^{3}(\fbox{195}x^{2}-96x+50)\)