How Do You Differentiate the Product of Two Functions Using the Chain Rule?

[ahazen]

I am trying to differentiate ((5x-1)^4)((8x^2-5)^-3) but i am stuck at a certain point...
Can you please help me fill in the blanks?

Thank you so much:):)


Work done:
1st step: (5x-1)^4 d/dx (8x^2-5)^-3 + (8x^2-5)^-3 d/dx(5x-1)^4

2nd step: (5x-1)^4 (-3)(8x^2-5)^-4 (16x)(8x^2-5)^-3 + (4)(5x-1)^3 (5)

3rd step: (I don't know what goes here...something x) (5x-1)^4 (8x^2-5)^-4 +9(5x-1)^4 (8x^2-5)^-3

Answer: 4(5x-4)^3 (8x^2-5)^-4 (I don't know what goes here)

 

[MaxManus]

f = ((5x-1)^4)((8x^2-5)^-3)
f' = ((5x-1)^4)'(8x^2-5)^-3) + ((5x-1)^4)((8x^2-5)^-3)'
f' = (4*5(5x-1)^3)(8x^2-5)^-3) + ((5x-1)^4)(16x*(-3)(8x^2-5)^-4)
simplify
f' = 20((5x-1)^3)((8x^2-5)^-3) -48x((5x-1)^4)((8x^2-5)^-4)
f' = ((5x-1)^3)((8x^2-5)^-4)(-80x^2+48x -100)

Not sure if this helps