calculus help please (derivatives)?

Question

what is the derivative of (√5-8x)/ (2x-7)^(1/3)?

thanks

can you show the work please?

Answer 1

assuming that's √(5 - 8x), let's use some shortcuts to simplify all the typing until we're done. let r = √(5 - 8x) and c = (2x - 7)^(1/3).

so dr/dx = -8 / 2r = -4/r and dc/dx = 2/(3c²), and using "lo dee hi - hi dee lo over lo squared"

d(r/c)/dx = [ c • -4/r - r • 2/(3c²) ] / c²
d(r/c)/dx = -4/(cr) - 2r/(3c^4)

then plug back in the radicals for c and r.

and lo, my TI-89 agrees.

Answer 2

is the sqr root inside the bracket or outside
like this (√5-8x)
or like this √(5-8x)

apply quotient rule

f(x)/g(x) =[ f'(x)g(x)-f(x)g'(x)] / [(g(x))²]

Answer 3

Quotient rule.