Asked by quarantine
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:
sin(x+y)=4x−4y at the point (π,π).
Tangent Line Equation:
Answers
Answered by
Reiny
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
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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