Question

use implicit differentiation to find y' if lnxy +5x=30

Answer 1

use it then ... what part are you getting stuck at?

Answer 2

the lnxy

Answer 3

consider lnu, how would you approach its derivative?

Answer 4

1/u(u')

Answer 5

good, but to avoid some amibuity: u'/u

let u = xy

what is u'? think product rule

Answer 6

**ambiguity...

Answer 7

Or you can say ln(xy) = ln(x) + ln(y).

Answer 8

ok so 1/x + 1/y(y')

Answer 9

y'/y. Yes.

Answer 10

my way:

u = xy

u' = x'y + xy'
= y + xy'

but yes, if you go the lnx + lny approach that would be fine as well

Answer 11

and5x is just ln 1/x correct?

Answer 12

No.

Answer 13

or 5

Answer 14

Of course.

Answer 15

30 is 0

Answer 16

so i got -y-5xy/x