Find the slope of the tangent line to xtany = y-1 at y=pi/4

Question

anonymous · Answer

Can anyone show the steps as well?

lgbasallote · Answer

i hated calculus but...slope of tangent means double derivative right?

anonymous · Answer

naw... just derivative

anonymous · Answer

are you differentiating with respect to x or y?

lgbasallote · Answer

but tangent is derivative right @dpaInc and slope is also derivative....right? or did i recall wrong :/

anonymous · Answer

it's just the first derivative....

anonymous · Answer

tangent is the line that kisses the curve at one point

derivative is the slope of that line

anonymous · Answer

Im not sure @Hermeezey but the answer is 2/6-pi

anonymous · Answer

you'll have to take the derivative implicitly since it is a hassle to do it explicitly..

anonymous · Answer

xtany = y-1
derive the whole thing with respect to x, then solve for dy/dx
tany + xsec^2y (dy/dx) = (dy/dx)
xsec^2y(dy/dx) - (dy/dx) = -tany
(dy/dx)(xsec^2y - 1) = -tany
(dy/dx) = (-tany)/(xsec^2y - 1)

anonymous · Answer

Solve for y when x = pi/4. Plug x and y into
dy/dx = (-tany)/(xsec^2y - 1) to get the slope of the tangent at that point.

anonymous · Answer

|dw:1334707662086:dw|
solve for y' here...