Wolfram Function Repository
Instantuse addon functions for the Wolfram Language
Function Repository Resource:
Compute properties of the tangent line to a curve at a given point
ResourceFunction["TangentLine"][expr,{x,a},{y,b}] gives an association of properties of the tangent line to expr, viewed as an equation in x and y, at the point {x,y}={a,b}. 

ResourceFunction["TangentLine"][expr,{x,a},{y,b},prop] returns the value of the tangent line property prop. 

ResourceFunction["TangentLine"][expr,{x,a},y,…] returns information relating to one, among possibly several, of the tangent lines to expr at x=a. 
Compute the slopeintercept equation of the tangent line to a curve at a given point:
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Visualize this result:
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Compute the slope of this tangent line:
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Compute the horizontal intercept of this tangent line:
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Get the standardform equation of this tangent line:
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Get an association of properties of a tangent line to a curve:
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Get just the pointslope equation of this tangent line:
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The first argument to TangentLine can be an implicit definition of a curve:
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If a tangent line coincides with a coordinate axis, its intercept with that axis is the set of real numbers:
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If a tangent line is parallel to, but does not coincide with, a coordinate axis, its intercept with that axis is None:
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Requesting tangent line information about a point that is not on the curve will result in an error message:
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Vertical tangent lines (whose slope cannot be computed) are excluded from the results returned by TangentLine:
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This result is despite the fact that this expression has a vertical tangent line at the origin:
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If y is not specified, information on only one of the possible tangent lines at is returned:
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To instead choose the other tangent line at , specify the corresponding value of y:
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