how to differentiate Y=(-3x+4)(4X^5+5)^-5

Question

anonymous · Answer

use the product rule i.e. d(u*v) = du*v + u*dv
you'll also have to use to chain rule on that second part (the v)

anonymous · Answer

well I just can't seem to simplify the second part: (4x^5+5)^-5 times -3

anonymous · Answer

the answer is 288x^5-400x^4-15/(4x^5+5)^6   which I am not getting...

anonymous · Answer

no need to simplify it any further or multiply it out; 
it's already in simple form

anonymous · Answer

ok let's see

anonymous · Answer

dy = (-3)(4X^5+5)^-5 + (20x)(-3x+4)(-5)(4X^5+5)^-6
    if you multiply that out should be right from eqn that you have written, but doesn't seem to match result you have?

anonymous · Answer

you could use quotient rule also cause of negative exponent in second term, but still wouldn't get your answer, hmmm...

anonymous · Answer

Yes, this problem has  been annoying me...