Question

tan(xy)=x , find dy/dx

Answer 1

implicit? It's been awhile

Answer 2

Implicit differentiation... hmm... let's find the derivative of both sides :)

Answer 3

yea implicit

Answer 4

yes.
i think it is
\[(xy' + y) (\sec^2(xy))=1\]

Answer 5

Yep

Answer 6

now just solve for dy/dx

Answer 7

which is the same as y'

Answer 8

so
\[xy' + y = 1 / \sec^2(xy)\] ?

Answer 9

Then subtract y from both sides then divide x from both sides

Answer 10

Ok. I don't know how to make it look like the answer choices.

Answer 11

\[(1-ytan(xy)\sec(xy) )/ xtan(xy)\sec(xy)\]
\[\frac{ \sec^2(xy)-y }{ x }\]
\[\cos^2(xy)\]
\[\frac{ \cos^2(xy)-y }{ x}\]
\[\frac{ \cos^2(xy) }{ x }\]

Answer 12

It's the second last one

Answer 13

Because 1/sec(x) is cos(x)

Answer 14

ahh ok. thanks!