Question

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

Answer 1

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)

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

ok let's see

Answer 6

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?

Answer 7

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

Answer 8

Yes, this problem has been annoying me...