# calculus

Use implicit differentiation to find an equation of the tangent line to the curve.

sin(x+y)=4x−4y at the point (π,π).

Tangent Line Equation:

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1. sin(x+y)=4x−4y
cos(x+y)(1 + dy/dx) = 4 - 4dy/dx
cos(x+y) + (dy/dx)cos(x+y) = 4 - 4dy/dx
(dy/dx)[cos(x+y) + 4] = 4 - cos(x+y)
dy/dx = (4 - cos(x+y))/(cos(x+y) + 4)
at (π,π)
dy/dx = (4 - cos(2π))/(cos(2π) + 4)
= (4-1)/(1 + 4) = 3/5

y - π = (3/5)(x - π)
change to whichever variation you need

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Reiny

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