inverse trig (2 Viewers)

[shuning]

if y =arc tan (e^x)

prove that dy/dx = 1/2 sin2y

 

[Drongoski]

if y =arc tan (e^x)

prove that dy/dx = 1/2 sin2y

y = arctan (e^x)

tan y = e^x

d/dx both sides (implicitly):

sec^2y dy/dx = e^x = tan y

dy/dx = tan y/ sec^2 y = (sin y/cos y) x cos^2 y = sin y cos y

= 1/2 (2 sin y cos y) = 1/2 sin 2y

 

[Drongoski]