Question

Find dy: (x)/√(7x-4). Please show steps!

Answer 1

multiply the top and the bottom by the reciprical

(7x+4)^(1/2)

Answer 2

do they want the derivative?

Answer 3

Yes, the answer is 7x-8/2(7x-4)^(3/2(
i don't know how they got 7x-8!! :(

Answer 4

do you want to use quient rule or product rule?

Answer 5

I prefer product rule

Answer 6

It doesn't really matter, since it's practically the same thing!

Answer 7

yeah but some teachers are nazis about use of quient rule for questions such as these


so we have

f(x) = (x)(7x-4)^(-1/2)


g(x) = x
g'(x) = 1


s(x) = (7x-4)^(-1/2)
s'(x) = -1/(2(7x-4)^(3/2)) * (7)
CHAIN RULE to find s'(x)

d(x) = x^(-1/2)
d'(x) = -1/(2x^(3/2))

l(x) = 7x-4
l'(x) = 7

s'(x) = d'(l(x)) * l'(x)

so now we apply product rule

g'(x)s(x) + g(x)s'(x)

so

(7x-4)^(-1/2) + x(-1/(2(7x-4)^(3/2)) * (7))

Answer 8

best to do derivatives the long way like I have when you first start out until you can do them in your head

Answer 9

just split things into smaller functions and apply the rules

Answer 10

Yes, I got to this part: (7x-4)^(-1/2) + x(-1/(2(7x-4)^(3/2)) * (7))
but how did they get 7x-8 in the numerator?

Answer 11

What I'm trying to ask is how did they combine those two?

Answer 12

you know about negative exponents right?