Find the slope of the tangent line to the ellipse given by x2 + 4y2 = 4 at the point (√2, -1/√2)

Question

anonymous · Answer

implicit differentiation

anonymous · Answer

$$2x+8y \frac{dy}{dx}=0$$

anonymous · Answer

$$8y \frac{dy}{dx}=-2x$$

anonymous · Answer

$$\frac{dy}{dx}=\frac{-2x}{8y}$$

anonymous · Answer

reduce and substitute x and y into derivative to get slope

anonymous · Answer

but when using the long way, it came out to be -1/2  and the answer should be 1/2 when using implicit differentiation

anonymous · Answer

anonymous · Answer

I got -1/2 through implicit... make sure you subtract 2x from both sides to get the negative.

anonymous · Answer

anonymous · Answer

oops

anonymous · Answer

see

anonymous · Answer

yeah, I got 1/2

anonymous · Answer

negative from derivative and negative in the y term make positive

anonymous · Answer

did that help you any

anonymous · Answer

???

anonymous · Answer

that is implicit differentiation,  but when i do it in the other way, it came out to be an opposite sign answer