Question

differentiate implicitly: sec^2 y - tan^2 x=1

Answer 1

\[\sec ^{2}y=1+\tan ^{2}x,1+\tan ^{2}y=1+\tan ^{2}x,2\tan y \sec ^{2}y \frac{ dy }{dx }=2\tan x \sec ^{2}x \]
\[\frac{ dy }{dx }=\frac{ \tan x \sec ^{2}x }{ \tan y \sec ^{2} y}\]

Answer 2

\[\frac{ dy }{ dx }=\frac{ \tan x \left( 1+\tan ^{2}x \right) }{\tan y \left( 1+\tan ^{2}x \right) }\]
\[=\frac{ \tan x }{\tan y }\]

Answer 3

wait, but for the denominator, would that be tany(1+tan^2y)?

Answer 4

\[given \sec ^{2}y-\tan ^{2}x=1,\sec ^{2}y=1+\tan ^{2}x\]