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What is the slope of the line tangent to the curve y+2=(x^2/

## What is the slope of the line tangent to the curve y+2=(x^2/

[From: Mathematics] [author: ] [Date: 01-07] [Hit: ]
What is the slope of the line tangent to the curve y+2=(x^2/2)-2sin(y) at the point (2,0)?I don’t even know where to start so if you could show all work or explain that would be great......

What is the slope of the line tangent to the curve y+2=(x^2/2)-2sin(y) at the point (2,0)?
I don’t even know where to start so if you could show all work or explain that would be great
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MyRank say: y + 2 = (x²/2)-2siny at point (2, 0)

dy/dx + 0 = 2x/2 - 2cosy.dy/dx

dy/dx = x-2cosy dy/dx

dy/dx + 2cosy.dy/dx = x

dy/dx (1+2cosy) = x

dy/dx = (x/1 + 2cosy) / (2, 0)

= 2/1 + 2cos0 = 2/3.
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khalil say: take a differential
dy = 2xdx / 2 - 2 cos(y) dy
dy / dx = x / ( 1 + 2cos(y))
dy / dx = 2 / ( 1 + 2cos(0))
dy / dx = 2/3
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Φ² = Φ+1 say: dy/dx = x - 2cos(y) dy/dx
dy/dx(1 + 2cos(y)) = x
dy/dx = x/(1 + 2cos(y))

at (2,0), m = dy/dx = 2/(1 + 2cos(0)) = 2/(1 + 2) = 2/3
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Captain Matticus, LandPiratesInc say: Derive implicitly

y + 2 = (1/2) * x^2 - 2 * sin(y)
dy + 0 = (1/2) * 2x * dx - 2 * cos(y) * dy
dy = x * dx - 2 * cos(y) * dy

x = 2 , y = 0

dy = 2 * dx - 2 * cos(0) * dy
dy = 2 * dx - 2 * 1 * dy
dy = 2 * dx - 2 * dy
dy + 2 * dy = 2 * dx
3 * dy = 2 * dx
3 * dy/dx = 2
dy/dx = 2/3
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